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Analysis in Banach Spaces : Volume III: Harmonic Analysis and Spectral Theory / / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
| Analysis in Banach Spaces : Volume III: Harmonic Analysis and Spectral Theory / / by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis |
| Autore | Hytönen Tuomas |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (839 pages) |
| Disciplina | 515.732 |
| Altri autori (Persone) |
van NeervenJan
VeraarMark WeisLutz |
| Collana | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Soggetto topico |
Functional analysis
Fourier analysis Harmonic analysis Operator theory Mathematical analysis Functional Analysis Fourier Analysis Abstract Harmonic Analysis Operator Theory Analysis Anàlisi harmònica Teoria d'operadors Anàlisi de Fourier Anàlisi matemàtica Anàlisi funcional Espais de Banach |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-46598-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 11 Singular integral operators -- 12 Dyadic operators and the T (1) theorem -- 13 The Fourier transform and multipliers -- 14 Function spaces -- 15 Bounded imaginary powers -- 16 The H∞-functional calculus revisited -- 17 Maximal regularity -- 18 Nonlinear parabolic evolution equations in critical spaces -- Appendix Q: Questions -- Appendix K: Semigroup theory revisited -- Appendix L: The trace method for real interpolation theory. |
| Record Nr. | UNINA-9910770276503321 |
Hytönen Tuomas
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differentiability in Banach spaces, differential forms and applications / / Celso Melchiades Doria
| Differentiability in Banach spaces, differential forms and applications / / Celso Melchiades Doria |
| Autore | Doria Celso Melchiades |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (369 pages) |
| Disciplina | 515.732 |
| Soggetto topico |
Banach spaces
Espais de Banach Stokes' theorem |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-77834-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Introduction -- Contents -- 1 Differentiation in mathbbRn -- 1 Differentiability of Functions f:mathbbRnrightarrowmathbbR -- 1.1 Directional Derivatives -- 1.2 Differentiable Functions -- 1.3 Differentials -- 1.4 Multiple Derivatives -- 1.5 Higher Order Differentials -- 2 Taylor's Formula -- 3 Critical Points and Local Extremes -- 3.1 Morse Functions -- 4 The Implicit Function Theorem and Applications -- 5 Lagrange Multipliers -- 5.1 The Ultraviolet Catastrophe: The Dawn of Quantum Mechanics -- 6 Differentiable Maps I -- 6.1 Basics Concepts -- 6.2 Coordinate Systems -- 6.3 The Local Form of an Immersion -- 6.4 The Local Form of Submersions -- 6.5 Generalization of the Implicit Function Theorem -- 7 Fundamental Theorem of Algebra -- 8 Jacobian Conjecture -- 8.1 Case n=1 -- 8.2 Case nge2 -- 8.3 Covering Spaces -- 8.4 Degree Reduction -- 2 Linear Operators in Banach Spaces -- 1 Bounded Linear Operators on Normed Spaces -- 2 Closed Operators and Closed Range Operators -- 3 Dual Spaces -- 4 The Spectrum of a Bounded Linear Operator -- 5 Compact Linear Operators -- 6 Fredholm Operators -- 6.1 The Spectral Theory of Compact Operators -- 7 Linear Operators on Hilbert Spaces -- 7.1 Characterization of Compact Operators on Hilbert Spaces -- 7.2 Self-adjoint Compact Operators on Hilbert Spaces -- 7.3 Fredholm Alternative -- 7.4 Hilbert-Schmidt Integral Operators -- 8 Closed Unbounded Linear Operators on Hilbert Spaces -- 3 Differentiation in Banach Spaces -- 1 Maps on Banach Spaces -- 1.1 Extension by Continuity -- 2 Derivation and Integration of Functions f:[a,b]rightarrowE -- 2.1 Derivation of a Single Variable Function -- 2.2 Integration of a Single Variable Function -- 3 Differentiable Maps II -- 4 Inverse Function Theorem (InFT) -- 4.1 Prelude for the Inverse Function Theorem -- 4.2 InFT for Functions of a Single Real Variable.
4.3 Proof of the Inverse Function Theorem (InFT) -- 4.4 Applications of InFT -- 5 Classical Examples in Variational Calculus -- 5.1 Euler-Lagrange Equations -- 5.2 Examples -- 6 Fredholm Maps -- 6.1 Final Comments and Examples -- 7 An Application of the Inverse Function Theorem to Geometry -- 4 Vector Fields -- 1 Vector Fields in mathbbRn -- 2 Conservative Vector Fields -- 3 Existence and Uniqueness Theorem for ODE -- 4 Flow of a Vector Field -- 5 Vector Fields as Differential Operators -- 6 Integrability, Frobenius Theorem -- 7 Lie Groups and Lie Algebras -- 8 Variations over a Flow, Lie Derivative -- 9 Gradient, Curl and Divergent Differential Operators -- 5 Vector Integration, Potential Theory -- 1 Vector Calculus -- 1.1 Line Integral -- 1.2 Surface Integral -- 2 Classical Theorems of Integration -- 2.1 Interpretation of the Curl and Div Operators -- 3 Elementary Aspects of the Theory of Potential -- 6 Differential Forms, Stokes Theorem -- 1 Exterior Algebra -- 2 Orientation on V and on the Inner Product on Λ(V) -- 2.1 Orientation -- 2.2 Inner Product in Λ(V) -- 2.3 Pseudo-Inner Product, the Lorentz Form -- 3 Differential Forms -- 3.1 Exterior Derivative -- 4 De Rham Cohomology -- 4.1 Short Exact Sequence -- 5 De Rham Cohomology of Spheres and Surfaces -- 6 Stokes Theorem -- 7 Orientation, Hodge Star-Operator and Exterior Co-derivative -- 8 Differential Forms on Manifolds, Stokes Theorem -- 8.1 Orientation -- 8.2 Integration on Manifolds -- 8.3 Exterior Derivative -- 8.4 Stokes Theorem on Manifolds -- 7 Applications to the Stokes Theorem -- 1 Volumes of the (n+1)-Disk and of the n-Sphere -- 2 Harmonic Functions -- 2.1 Laplacian Operator -- 2.2 Properties of Harmonic Functions -- 3 Poisson Kernel for the n-Disk DnR -- 4 Harmonic Differential Forms -- 4.1 Hodge Theorem on Manifolds -- 5 Geometric Formulation of the Electromagnetic Theory. 5.1 Electromagnetic Potentials -- 5.2 Geometric Formulation -- 5.3 Variational Formulation -- 6 Helmholtz's Decomposition Theorem -- Appendix A Basics of Analysis -- 1 Sets -- 2 Finite-dimensional Linear Algebra: V=mathbbRn -- 2.1 Matrix Spaces -- 2.2 Linear Transformations -- 2.3 Primary Decomposition Theorem -- 2.4 Inner Product and Sesquilinear Forms -- 2.5 The Sylvester Theorem -- 2.6 Dual Vector Spaces -- 3 Metric and Banach Spaces -- 4 Calculus Theorems -- 4.1 One Real Variable Functions -- 4.2 Functions of Several Real Variables -- 5 Proper Maps -- 6 Equicontinuity and the Ascoli-Arzelà Theorem -- 7 Functional Analysis Theorems -- 7.1 Riesz and Hahn-Banach Theorems -- 7.2 Topological Complementary Subspace -- 8 The Contraction Lemma -- Appendix B Differentiable Manifolds, Lie Groups -- 1 Differentiable Manifolds -- 2 Bundles: Tangent and Cotangent -- 3 Lie Groups -- Appendix C Tensor Algebra -- 1 Tensor Product -- 2 Tensor Algebra -- Appendix References -- -- Index. |
| Record Nr. | UNINA-9910495154603321 |
|
Doria Celso Melchiades
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differentiability in Banach spaces, differential forms and applications / / Celso Melchiades Doria
| Differentiability in Banach spaces, differential forms and applications / / Celso Melchiades Doria |
| Autore | Doria Celso Melchiades |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (369 pages) |
| Disciplina | 515.732 |
| Soggetto topico |
Banach spaces
Espais de Banach Stokes' theorem |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-77834-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Introduction -- Contents -- 1 Differentiation in mathbbRn -- 1 Differentiability of Functions f:mathbbRnrightarrowmathbbR -- 1.1 Directional Derivatives -- 1.2 Differentiable Functions -- 1.3 Differentials -- 1.4 Multiple Derivatives -- 1.5 Higher Order Differentials -- 2 Taylor's Formula -- 3 Critical Points and Local Extremes -- 3.1 Morse Functions -- 4 The Implicit Function Theorem and Applications -- 5 Lagrange Multipliers -- 5.1 The Ultraviolet Catastrophe: The Dawn of Quantum Mechanics -- 6 Differentiable Maps I -- 6.1 Basics Concepts -- 6.2 Coordinate Systems -- 6.3 The Local Form of an Immersion -- 6.4 The Local Form of Submersions -- 6.5 Generalization of the Implicit Function Theorem -- 7 Fundamental Theorem of Algebra -- 8 Jacobian Conjecture -- 8.1 Case n=1 -- 8.2 Case nge2 -- 8.3 Covering Spaces -- 8.4 Degree Reduction -- 2 Linear Operators in Banach Spaces -- 1 Bounded Linear Operators on Normed Spaces -- 2 Closed Operators and Closed Range Operators -- 3 Dual Spaces -- 4 The Spectrum of a Bounded Linear Operator -- 5 Compact Linear Operators -- 6 Fredholm Operators -- 6.1 The Spectral Theory of Compact Operators -- 7 Linear Operators on Hilbert Spaces -- 7.1 Characterization of Compact Operators on Hilbert Spaces -- 7.2 Self-adjoint Compact Operators on Hilbert Spaces -- 7.3 Fredholm Alternative -- 7.4 Hilbert-Schmidt Integral Operators -- 8 Closed Unbounded Linear Operators on Hilbert Spaces -- 3 Differentiation in Banach Spaces -- 1 Maps on Banach Spaces -- 1.1 Extension by Continuity -- 2 Derivation and Integration of Functions f:[a,b]rightarrowE -- 2.1 Derivation of a Single Variable Function -- 2.2 Integration of a Single Variable Function -- 3 Differentiable Maps II -- 4 Inverse Function Theorem (InFT) -- 4.1 Prelude for the Inverse Function Theorem -- 4.2 InFT for Functions of a Single Real Variable.
4.3 Proof of the Inverse Function Theorem (InFT) -- 4.4 Applications of InFT -- 5 Classical Examples in Variational Calculus -- 5.1 Euler-Lagrange Equations -- 5.2 Examples -- 6 Fredholm Maps -- 6.1 Final Comments and Examples -- 7 An Application of the Inverse Function Theorem to Geometry -- 4 Vector Fields -- 1 Vector Fields in mathbbRn -- 2 Conservative Vector Fields -- 3 Existence and Uniqueness Theorem for ODE -- 4 Flow of a Vector Field -- 5 Vector Fields as Differential Operators -- 6 Integrability, Frobenius Theorem -- 7 Lie Groups and Lie Algebras -- 8 Variations over a Flow, Lie Derivative -- 9 Gradient, Curl and Divergent Differential Operators -- 5 Vector Integration, Potential Theory -- 1 Vector Calculus -- 1.1 Line Integral -- 1.2 Surface Integral -- 2 Classical Theorems of Integration -- 2.1 Interpretation of the Curl and Div Operators -- 3 Elementary Aspects of the Theory of Potential -- 6 Differential Forms, Stokes Theorem -- 1 Exterior Algebra -- 2 Orientation on V and on the Inner Product on Λ(V) -- 2.1 Orientation -- 2.2 Inner Product in Λ(V) -- 2.3 Pseudo-Inner Product, the Lorentz Form -- 3 Differential Forms -- 3.1 Exterior Derivative -- 4 De Rham Cohomology -- 4.1 Short Exact Sequence -- 5 De Rham Cohomology of Spheres and Surfaces -- 6 Stokes Theorem -- 7 Orientation, Hodge Star-Operator and Exterior Co-derivative -- 8 Differential Forms on Manifolds, Stokes Theorem -- 8.1 Orientation -- 8.2 Integration on Manifolds -- 8.3 Exterior Derivative -- 8.4 Stokes Theorem on Manifolds -- 7 Applications to the Stokes Theorem -- 1 Volumes of the (n+1)-Disk and of the n-Sphere -- 2 Harmonic Functions -- 2.1 Laplacian Operator -- 2.2 Properties of Harmonic Functions -- 3 Poisson Kernel for the n-Disk DnR -- 4 Harmonic Differential Forms -- 4.1 Hodge Theorem on Manifolds -- 5 Geometric Formulation of the Electromagnetic Theory. 5.1 Electromagnetic Potentials -- 5.2 Geometric Formulation -- 5.3 Variational Formulation -- 6 Helmholtz's Decomposition Theorem -- Appendix A Basics of Analysis -- 1 Sets -- 2 Finite-dimensional Linear Algebra: V=mathbbRn -- 2.1 Matrix Spaces -- 2.2 Linear Transformations -- 2.3 Primary Decomposition Theorem -- 2.4 Inner Product and Sesquilinear Forms -- 2.5 The Sylvester Theorem -- 2.6 Dual Vector Spaces -- 3 Metric and Banach Spaces -- 4 Calculus Theorems -- 4.1 One Real Variable Functions -- 4.2 Functions of Several Real Variables -- 5 Proper Maps -- 6 Equicontinuity and the Ascoli-Arzelà Theorem -- 7 Functional Analysis Theorems -- 7.1 Riesz and Hahn-Banach Theorems -- 7.2 Topological Complementary Subspace -- 8 The Contraction Lemma -- Appendix B Differentiable Manifolds, Lie Groups -- 1 Differentiable Manifolds -- 2 Bundles: Tangent and Cotangent -- 3 Lie Groups -- Appendix C Tensor Algebra -- 1 Tensor Product -- 2 Tensor Algebra -- Appendix References -- -- Index. |
| Record Nr. | UNISA-996466394503316 |
|
Doria Celso Melchiades
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Optimization in Banach spaces / / Alexander J. Zaslavski
| Optimization in Banach spaces / / Alexander J. Zaslavski |
| Autore | Zaslavski Alexander J. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (132 pages) |
| Disciplina | 515.732 |
| Collana | SpringerBriefs in Optimization |
| Soggetto topico |
Banach spaces
Mathematical optimization Optimització matemàtica Espais de Banach |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031126444
9783031126437 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- 1 Introduction -- 1.1 Notation -- 1.2 Constrained Optimization -- 1.3 Unconstrained Optimization -- 1.4 An Auxiliary Result -- 1.5 Proof of Theorem 1.1 -- 2 Convex Optimization -- 2.1 Preliminaries -- 2.2 A basic Lemma -- 2.3 Convergence Results -- 2.4 Proof of Theorem 2.2 -- 2.5 Proof of Theorem 2.3 -- 2.6 Proof of Theorem 2.4 -- 2.7 Proof of Theorem 2.5 -- 2.8 Proof of Theorem 2.6 -- 2.9 Proof of Theorem 2.7 -- 2.10 Proof of Theorem 2.8 -- 2.11 Proof of Theorem 2.9 -- 2.12 Proof of Theorem 2.10 -- 2.13 A Convergence Result with Estimations -- 2.14 An Auxiliary Result -- 2.15 Proof of Theorem 2.11 -- 3 Nonconvex Optimization -- 3.1 Preliminaries -- 3.2 Auxiliary Results -- 3.3 Convergence Results -- 3.4 Proofs of Theorems 3.5-3.9 -- 3.5 Proofs of Theorems 3.10-3.14 -- 3.6 Proof of Theorem 3.15 -- 3.7 A Convergence Result with Estimations -- 3.8 An Auxiliary Result -- 3.9 Proofs of Theorems 3.16 and 3.17 -- 4 Continuous Algorithms -- 4.1 Banach Space Valued Functions -- 4.2 Convex Problems -- 4.3 Proof of Theorem 4.5 -- 4.4 Proof of Theorem 4.6 -- 4.5 Proof of Theorem 4.7 -- 4.6 The First Convergence Result with Estimations -- 4.7 Nonconvex Optimization -- 4.8 Convergence Results -- 4.9 Proof of Theorem 4.11 -- 4.10 Proofs of Theorems 4.12 and 4.14 -- 4.11 Proof of Theorem 4.15 -- 4.12 Proof of Theorem 4.17 -- 4.13 The Second Convergence Result with Estimations -- References. |
| Record Nr. | UNISA-996490344803316 |
|
Zaslavski Alexander J.
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Optimization in Banach spaces / / Alexander J. Zaslavski
| Optimization in Banach spaces / / Alexander J. Zaslavski |
| Autore | Zaslavski Alexander J. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (132 pages) |
| Disciplina | 515.732 |
| Collana | SpringerBriefs in Optimization |
| Soggetto topico |
Banach spaces
Mathematical optimization Optimització matemàtica Espais de Banach |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031126444
9783031126437 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- 1 Introduction -- 1.1 Notation -- 1.2 Constrained Optimization -- 1.3 Unconstrained Optimization -- 1.4 An Auxiliary Result -- 1.5 Proof of Theorem 1.1 -- 2 Convex Optimization -- 2.1 Preliminaries -- 2.2 A basic Lemma -- 2.3 Convergence Results -- 2.4 Proof of Theorem 2.2 -- 2.5 Proof of Theorem 2.3 -- 2.6 Proof of Theorem 2.4 -- 2.7 Proof of Theorem 2.5 -- 2.8 Proof of Theorem 2.6 -- 2.9 Proof of Theorem 2.7 -- 2.10 Proof of Theorem 2.8 -- 2.11 Proof of Theorem 2.9 -- 2.12 Proof of Theorem 2.10 -- 2.13 A Convergence Result with Estimations -- 2.14 An Auxiliary Result -- 2.15 Proof of Theorem 2.11 -- 3 Nonconvex Optimization -- 3.1 Preliminaries -- 3.2 Auxiliary Results -- 3.3 Convergence Results -- 3.4 Proofs of Theorems 3.5-3.9 -- 3.5 Proofs of Theorems 3.10-3.14 -- 3.6 Proof of Theorem 3.15 -- 3.7 A Convergence Result with Estimations -- 3.8 An Auxiliary Result -- 3.9 Proofs of Theorems 3.16 and 3.17 -- 4 Continuous Algorithms -- 4.1 Banach Space Valued Functions -- 4.2 Convex Problems -- 4.3 Proof of Theorem 4.5 -- 4.4 Proof of Theorem 4.6 -- 4.5 Proof of Theorem 4.7 -- 4.6 The First Convergence Result with Estimations -- 4.7 Nonconvex Optimization -- 4.8 Convergence Results -- 4.9 Proof of Theorem 4.11 -- 4.10 Proofs of Theorems 4.12 and 4.14 -- 4.11 Proof of Theorem 4.15 -- 4.12 Proof of Theorem 4.17 -- 4.13 The Second Convergence Result with Estimations -- References. |
| Record Nr. | UNINA-9910616207103321 |
|
Zaslavski Alexander J.
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
P-adic banach space representations : with applications to principal series / / Dubravka Ban
| P-adic banach space representations : with applications to principal series / / Dubravka Ban |
| Autore | Ban Dubravka |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] |
| Descrizione fisica | 1 online resource (219 pages) |
| Disciplina | 515.732 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Banach spaces
p-adic analysis Espais de Banach Anàlisi p-àdica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031226847
9783031226830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Admissible Banach Space Representations -- 1.2 Principal Series Representations -- 1.3 Some Questions and Further Reading -- 1.4 Prerequisites -- 1.5 Notation -- 1.6 Groups -- Part I Banach Space Representations of p-adic Lie Groups -- 2 Iwasawa Algebras -- 2.1 Projective Limits -- 2.1.1 Universal Property of Projective Limits -- 2.1.2 Projective Limit Topology -- Cofinal Subsystem -- Morphisms of Inverse Systems -- 2.2 Projective Limits of Topological Groups and oK-Modules -- 2.2.1 Profinite Groups -- Topology on Profinite Groups -- 2.3 Iwasawa Rings -- 2.3.1 Linear-Topological oK-Modules -- Definition of Iwasawa Algebra -- Fundamental System of Neighborhoods of Zero -- Embedding oK[G0], G0, and oK into oK[[G0]] -- 2.3.2 Another Projective Limit Realization of oK[[G0]] -- 2.3.3 Some Properties of Iwasawa Algebras -- Zero Divisors -- Augmentation Map -- Iwasawa Algebra of a Subgroup -- 3 Distributions -- 3.1 Locally Convex Vector Spaces -- 3.1.1 Banach Spaces -- 3.1.2 Continuous Linear Operators -- 3.1.3 Examples of Banach Spaces -- Banach Space of Bounded Functions -- Continuous Functions on G0 -- Mahler Expansion -- 3.1.4 Double Duals of a Banach Space -- 3.2 Distributions -- 3.2.1 The Weak Topology on Dc(G0,oK) -- 3.2.2 Distributions and Iwasawa Rings -- 3.2.3 The Canonical Pairing -- 3.3 The Bounded-Weak Topology -- 3.3.1 The Bounded-Weak Topology is Strictly Finer than the Weak Topology -- The Weak Topology on V' -- The Bounded-Weak Topology on V' -- 3.4 Locally Convex Topology on K[[G0]] -- 3.4.1 The Canonical Pairing -- 3.4.2 p-adic Haar Measure -- 3.4.3 The Ring Structure on Dc(G0,K) -- A Big Projective Limit -- 4 Banach Space Representations -- 4.1 p-adic Lie Groups -- 4.2 Linear Operators on Banach Spaces -- 4.2.1 Spherically Complete Spaces.
4.2.2 Some Fundamental Theorems in Functional Analysis -- 4.2.3 Banach Space Representations: Definition and Basic Properties -- 4.3 Schneider-Teitelbaum Duality -- 4.3.1 Schikhof's Duality -- 4.3.2 Duality for Banach Space Representations: Iwasawa Modules -- K[[G0]]-module structure on V' -- 4.4 Admissible Banach Space Representations -- 4.4.1 Locally Analytic Vectors: Representations in Characteristic p -- Locally Analytic Vectors -- Unitary Representations and Reduction Modulo pK -- 4.4.2 Duality for p-adic Lie Groups -- Part II Principal Series Representations of Reductive Groups -- Notation in Part II -- 5 Reductive Groups -- 5.1 Linear Algebraic Groups -- 5.1.1 Basic Properties of Linear Algebraic Groups -- More Examples of Linear Algebraic Groups -- Unipotent Subgroups -- Identity Component -- Tori -- 5.1.2 Lie Algebra of an Algebraic Group -- Lie Algebras -- Lie Algebra of an Algebraic Group -- 5.2 Reductive Groups Over Algebraically Closed Fields -- 5.2.1 Rational Characters -- 5.2.2 Roots of a Reductive Group -- Weyl Group -- Abstract Root Systems -- Simple Roots -- 5.2.3 Classification of Irreducible Root Systems -- 5.2.4 Classification of Reductive Groups -- Cocharacters -- Root Datum of a Reductive Group -- Abstract Root Datum -- 5.2.5 Structure of Reductive Groups -- Root Subgroups -- Borel Subgroups and Parabolic Subgroups -- 5.3 F-Reductive Groups -- 5.4 Z-Groups -- 5.4.1 Algebraic R-Groups -- 5.4.2 Split Z-Groups -- Root Subgroups -- 5.5 The Structure of G(L) -- 5.5.1 oL-Points of Algebraic Z-Groups -- 5.5.2 oL-Points of Split Z-Groups -- 5.5.3 Coset Representatives for G/P -- 5.6 General Linear Groups -- 6 Algebraic and Smooth Representations -- 6.1 Algebraic Representations -- 6.1.1 Definition and Basic Properties -- 6.1.2 Classification of Simple Modules of Reductive Groups -- Abstract Weights -- Weights of a Reductive Group. Dominant Bases of X(T) -- Weights of a Module -- Algebraic Induction -- Simple Modules -- 6.2 Smooth Representations -- 6.2.1 Absolute Value -- 6.2.2 Smooth Representations and Characters -- 6.2.3 Basic Properties -- Isomorphic Fields -- Absolutely Irreducible Representations -- Contragredient -- Tensor Product of Representations -- 6.2.4 Admissible-Smooth Representations -- 6.2.5 Smooth Principal Series -- Normalized Induction -- Composition Factors of Principal Series -- 6.2.6 Smooth Principal Series of GL2(L) and SL2(L) -- 7 Continuous Principal Series -- 7.1 Continuous Principal Series Are Banach -- 7.1.1 Direct Sum Decomposition of IndP0G0(χ0-1) -- 7.1.2 Unitary Principal Series -- 7.1.3 Algebraic and Smooth Vectors -- Algebraic Characters -- Smooth Characters -- 7.1.4 Unitary Principal Series of GL2(Qp) -- 7.2 Duals of Principal Series -- 7.2.1 Module M0(χ) -- 7.3 Projective Limit Realization of M0(χ) -- 7.4 Direct Sum Decomposition of M(χ) -- 7.4.1 The Case G0=GL2(Zp) -- 7.4.2 General Case -- 8 Intertwining Operators -- 8.1 Invariant Distributions -- 8.1.1 Invariant Distributions on Vector Groups -- 8.1.2 ``Partially Invariant'' Distributions on Unipotent Groups -- 8.1.3 T0-Equivariant Distributions on Unipotent Groups -- 8.2 Intertwining Algebra -- 8.2.1 Ordinary Representations of GL2(Qp) -- 8.3 Finite Dimensional G0-Invariant Subspaces -- 8.3.1 Induction from the Trivial Character: Intertwiners -- 8.4 Reducibility of Principal Series -- 8.4.1 Locally Analytic Vectors -- Reducibility Question for G(Qp) -- Reducibility Question for G(L) -- 8.4.2 A Criterion for Irreducibility -- A Nonarchimedean Fields and Spaces -- A.1 Ultrametric Spaces -- A.2 Nonarchimedean Local Fields -- A.2.1 p-Adic Numbers -- A.2.2 Finite Extensions of Qp -- A.2.3 Algebraic Closure Qp -- A.3 Normed Vector Spaces -- B Affine and Projective Varieties. B.1 Affine Varieties -- B.1.1 Zariski Topology on Affine Space -- B.1.2 Morphisms and Products of Affine Varieties -- B.2 Projective Varieties -- References -- Index. |
| Record Nr. | UNISA-996511863103316 |
|
Ban Dubravka
|
||
| Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
P-adic banach space representations : with applications to principal series / / Dubravka Ban
| P-adic banach space representations : with applications to principal series / / Dubravka Ban |
| Autore | Ban Dubravka |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] |
| Descrizione fisica | 1 online resource (219 pages) |
| Disciplina | 515.732 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Banach spaces
p-adic analysis Espais de Banach Anàlisi p-àdica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031226847
9783031226830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Admissible Banach Space Representations -- 1.2 Principal Series Representations -- 1.3 Some Questions and Further Reading -- 1.4 Prerequisites -- 1.5 Notation -- 1.6 Groups -- Part I Banach Space Representations of p-adic Lie Groups -- 2 Iwasawa Algebras -- 2.1 Projective Limits -- 2.1.1 Universal Property of Projective Limits -- 2.1.2 Projective Limit Topology -- Cofinal Subsystem -- Morphisms of Inverse Systems -- 2.2 Projective Limits of Topological Groups and oK-Modules -- 2.2.1 Profinite Groups -- Topology on Profinite Groups -- 2.3 Iwasawa Rings -- 2.3.1 Linear-Topological oK-Modules -- Definition of Iwasawa Algebra -- Fundamental System of Neighborhoods of Zero -- Embedding oK[G0], G0, and oK into oK[[G0]] -- 2.3.2 Another Projective Limit Realization of oK[[G0]] -- 2.3.3 Some Properties of Iwasawa Algebras -- Zero Divisors -- Augmentation Map -- Iwasawa Algebra of a Subgroup -- 3 Distributions -- 3.1 Locally Convex Vector Spaces -- 3.1.1 Banach Spaces -- 3.1.2 Continuous Linear Operators -- 3.1.3 Examples of Banach Spaces -- Banach Space of Bounded Functions -- Continuous Functions on G0 -- Mahler Expansion -- 3.1.4 Double Duals of a Banach Space -- 3.2 Distributions -- 3.2.1 The Weak Topology on Dc(G0,oK) -- 3.2.2 Distributions and Iwasawa Rings -- 3.2.3 The Canonical Pairing -- 3.3 The Bounded-Weak Topology -- 3.3.1 The Bounded-Weak Topology is Strictly Finer than the Weak Topology -- The Weak Topology on V' -- The Bounded-Weak Topology on V' -- 3.4 Locally Convex Topology on K[[G0]] -- 3.4.1 The Canonical Pairing -- 3.4.2 p-adic Haar Measure -- 3.4.3 The Ring Structure on Dc(G0,K) -- A Big Projective Limit -- 4 Banach Space Representations -- 4.1 p-adic Lie Groups -- 4.2 Linear Operators on Banach Spaces -- 4.2.1 Spherically Complete Spaces.
4.2.2 Some Fundamental Theorems in Functional Analysis -- 4.2.3 Banach Space Representations: Definition and Basic Properties -- 4.3 Schneider-Teitelbaum Duality -- 4.3.1 Schikhof's Duality -- 4.3.2 Duality for Banach Space Representations: Iwasawa Modules -- K[[G0]]-module structure on V' -- 4.4 Admissible Banach Space Representations -- 4.4.1 Locally Analytic Vectors: Representations in Characteristic p -- Locally Analytic Vectors -- Unitary Representations and Reduction Modulo pK -- 4.4.2 Duality for p-adic Lie Groups -- Part II Principal Series Representations of Reductive Groups -- Notation in Part II -- 5 Reductive Groups -- 5.1 Linear Algebraic Groups -- 5.1.1 Basic Properties of Linear Algebraic Groups -- More Examples of Linear Algebraic Groups -- Unipotent Subgroups -- Identity Component -- Tori -- 5.1.2 Lie Algebra of an Algebraic Group -- Lie Algebras -- Lie Algebra of an Algebraic Group -- 5.2 Reductive Groups Over Algebraically Closed Fields -- 5.2.1 Rational Characters -- 5.2.2 Roots of a Reductive Group -- Weyl Group -- Abstract Root Systems -- Simple Roots -- 5.2.3 Classification of Irreducible Root Systems -- 5.2.4 Classification of Reductive Groups -- Cocharacters -- Root Datum of a Reductive Group -- Abstract Root Datum -- 5.2.5 Structure of Reductive Groups -- Root Subgroups -- Borel Subgroups and Parabolic Subgroups -- 5.3 F-Reductive Groups -- 5.4 Z-Groups -- 5.4.1 Algebraic R-Groups -- 5.4.2 Split Z-Groups -- Root Subgroups -- 5.5 The Structure of G(L) -- 5.5.1 oL-Points of Algebraic Z-Groups -- 5.5.2 oL-Points of Split Z-Groups -- 5.5.3 Coset Representatives for G/P -- 5.6 General Linear Groups -- 6 Algebraic and Smooth Representations -- 6.1 Algebraic Representations -- 6.1.1 Definition and Basic Properties -- 6.1.2 Classification of Simple Modules of Reductive Groups -- Abstract Weights -- Weights of a Reductive Group. Dominant Bases of X(T) -- Weights of a Module -- Algebraic Induction -- Simple Modules -- 6.2 Smooth Representations -- 6.2.1 Absolute Value -- 6.2.2 Smooth Representations and Characters -- 6.2.3 Basic Properties -- Isomorphic Fields -- Absolutely Irreducible Representations -- Contragredient -- Tensor Product of Representations -- 6.2.4 Admissible-Smooth Representations -- 6.2.5 Smooth Principal Series -- Normalized Induction -- Composition Factors of Principal Series -- 6.2.6 Smooth Principal Series of GL2(L) and SL2(L) -- 7 Continuous Principal Series -- 7.1 Continuous Principal Series Are Banach -- 7.1.1 Direct Sum Decomposition of IndP0G0(χ0-1) -- 7.1.2 Unitary Principal Series -- 7.1.3 Algebraic and Smooth Vectors -- Algebraic Characters -- Smooth Characters -- 7.1.4 Unitary Principal Series of GL2(Qp) -- 7.2 Duals of Principal Series -- 7.2.1 Module M0(χ) -- 7.3 Projective Limit Realization of M0(χ) -- 7.4 Direct Sum Decomposition of M(χ) -- 7.4.1 The Case G0=GL2(Zp) -- 7.4.2 General Case -- 8 Intertwining Operators -- 8.1 Invariant Distributions -- 8.1.1 Invariant Distributions on Vector Groups -- 8.1.2 ``Partially Invariant'' Distributions on Unipotent Groups -- 8.1.3 T0-Equivariant Distributions on Unipotent Groups -- 8.2 Intertwining Algebra -- 8.2.1 Ordinary Representations of GL2(Qp) -- 8.3 Finite Dimensional G0-Invariant Subspaces -- 8.3.1 Induction from the Trivial Character: Intertwiners -- 8.4 Reducibility of Principal Series -- 8.4.1 Locally Analytic Vectors -- Reducibility Question for G(Qp) -- Reducibility Question for G(L) -- 8.4.2 A Criterion for Irreducibility -- A Nonarchimedean Fields and Spaces -- A.1 Ultrametric Spaces -- A.2 Nonarchimedean Local Fields -- A.2.1 p-Adic Numbers -- A.2.2 Finite Extensions of Qp -- A.2.3 Algebraic Closure Qp -- A.3 Normed Vector Spaces -- B Affine and Projective Varieties. B.1 Affine Varieties -- B.1.1 Zariski Topology on Affine Space -- B.1.2 Morphisms and Products of Affine Varieties -- B.2 Projective Varieties -- References -- Index. |
| Record Nr. | UNINA-9910659490703321 |
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Ban Dubravka
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| Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Renormings in Banach spaces : a toolbox / / Antonio José Guirao, Vicente Montesinos and Václav Zizler
| Renormings in Banach spaces : a toolbox / / Antonio José Guirao, Vicente Montesinos and Václav Zizler |
| Autore | Guirao Antonio José |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2022] |
| Descrizione fisica | 1 online resource (621 pages) |
| Disciplina | 515.732 |
| Collana | Monografie matematyczne |
| Soggetto topico |
Banach spaces
Normed linear spaces Geometry Espais de Banach Espais vectorials normats |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-08655-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996485661403316 |
|
Guirao Antonio José
|
||
| Cham, Switzerland : , : Birkhäuser, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Renormings in Banach spaces : a toolbox / / Antonio José Guirao, Vicente Montesinos and Václav Zizler
| Renormings in Banach spaces : a toolbox / / Antonio José Guirao, Vicente Montesinos and Václav Zizler |
| Autore | Guirao Antonio José |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2022] |
| Descrizione fisica | 1 online resource (621 pages) |
| Disciplina | 515.732 |
| Collana | Monografie matematyczne |
| Soggetto topico |
Banach spaces
Normed linear spaces Geometry Espais de Banach Espais vectorials normats |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-08655-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910736984803321 |
|
Guirao Antonio José
|
||
| Cham, Switzerland : , : Birkhäuser, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Espais de Banach
(9)
- Banach spaces (8)
- Anàlisi p-àdica (2)
- Espais vectorials normats (2)
- Geometry (2)