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An Advanced Complex Analysis Problem Book : Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions / / by Daniel Alpay
| An Advanced Complex Analysis Problem Book : Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions / / by Daniel Alpay |
| Autore | Alpay Daniel |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2015 |
| Descrizione fisica | 1 online resource (IX, 521 p.) |
| Disciplina | 515.7 |
| Soggetto topico |
Functional analysis
Operator theory Functional Analysis Operator Theory |
| ISBN | 3-319-16059-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Prologue -- Part I, Analytic functions -- 1 Some algebra -- 2 Exercises in complex variables -- Part II, Topology and functional analysis -- 3 Topological spaces -- 4 Normed spaces -- 5 Locally convex topological vector spaces -- 6 Some functional analysis -- Part III, Hilbert spaces of analytic functions -- 7 Reproducing kernel Hilbert spaces -- 8 Hardy spaces -- 9 de Branges-Rovnyak spaces -- 10 Bergman spaces -- 11 Fock spaces -- Index -- Name index -- Notation index. |
| Record Nr. | UNINA-9910300256503321 |
Alpay Daniel
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis / / by Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
| Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis / / by Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa |
| Autore | Alpay Daniel |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (107 p.) |
| Disciplina | 515.7 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Functions of complex variables
Functional analysis Operator theory System theory Functions of a Complex Variable Functional Analysis Operator Theory Systems Theory, Control |
| ISBN | 3-319-05110-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Bicomplex and hyperbolic numbers -- 2. Bicomplex functions and matrices -- 3. BC-modules -- 4. Norms and inner products on BC-modules -- 5. Linear functionals and linear operators on BC-modules -- 6. Schur analysis. |
| Record Nr. | UNINA-9910299962003321 |
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Alpay Daniel
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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A Complex Analysis Problem Book / / by Daniel Alpay
| A Complex Analysis Problem Book / / by Daniel Alpay |
| Autore | Alpay Daniel |
| Edizione | [2nd ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 |
| Descrizione fisica | 1 online resource (X, 596 p.) |
| Disciplina | 515.9 |
| Soggetto topico |
Functions of complex variables
Functions of a Complex Variable |
| ISBN | 3-319-42181-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I Complex Numbers -- Complex Numbers: Algebra -- Complex Numbers: Geometry -- Complex Numbers and Analysis -- Part II Functions of a Complex Variable -- Cauchy–Riemann Equations and C-differentiable Functions -- Cauchy’sTheorem -- Morera, Liouville, Schwarz, et les autres: First Applications -- Laurent Expansions, Residues, Singularities and Applications -- Computations of Definite Integrals Using the Residue Theorem -- Part III Applications and More Advanced Topics -- Harmonic Functions -- Conformal Mappings -- A Taste of Linear System Theory and Signal Processing -- Rational Functions -- Special Functions and Transforms -- Part IV Appendix -- Some Topology -- Some Functional Analysis Essentials -- A Brief Survey of Integration. |
| Record Nr. | UNINA-9910254092203321 |
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Alpay Daniel
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Exercises in Applied Mathematics : With a View Toward Information Theory, Machine Learning, Wavelets, and Statistical Physics
| Exercises in Applied Mathematics : With a View Toward Information Theory, Machine Learning, Wavelets, and Statistical Physics |
| Autore | Alpay Daniel |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing AG, , 2024 |
| Descrizione fisica | 1 online resource (0 pages) |
| Disciplina | 515.076 |
| Collana | Chapman Mathematical Notes Series |
| ISBN | 3-031-51822-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Contents -- 1 Prologue -- 1.1 A Guide Throughout the Book -- 1.2 Introduction -- 1.3 The Source Partition Theorem: Entropy -- 1.4 Another Motivation for H -- 1.5 Shannon's Theorem for the Binary Symmetric Channel (BSC) -- 1.6 Repetition Code and Hamming Code -- 1.7 Maximum Entropy and a First Connection with Statistical Physics -- 1.8 The Case of Continuous Signals -- 1.9 Some Questions Related to Statistical Physics -- 1.10 Some Questions and Tools in Quantum Mechanics -- 1.11 Some Questions and Tools in Quantum Information Theory -- 1.12 Machine Learning -- 1.13 Solutions of the Exercises -- 1.14 Some Specific Exercises and Questions -- Part I Algebra -- 2 Complements in Linear Algebra -- 2.1 Complex Numbers -- 2.2 Beyond Complex Numbers -- 2.3 Vector Spaces and Linear Transformations -- 2.4 Hermitian Forms and Positive Operators -- 2.5 The Perceptron Convergence Theorem -- 2.6 The Scalar Case -- 2.7 Solutions of the Exercises -- 3 Positive Semi-Definite Matrices -- 3.1 Matrices -- 3.2 Schur Complement -- 3.3 Newton's Formulas -- 3.4 Hermitian Matrices -- 3.5 Positive Semi-Definite Matrices -- 3.6 Tensor Products and the Tensor Algebra -- 3.7 Completely Positive Maps -- 3.8 Maximum Entropy Analysis and the Yule-Walker Equation -- 3.9 Solutions of the Exercises -- 4 Algebra and Error-Correcting Codes -- 4.1 Sets, Functions, and Groups -- 4.2 Rings, Ideals, and Fields -- 4.3 Finite Fields -- 4.4 Splitting Field -- 4.5 Error-Correcting Codes: Generalities -- 4.6 Linear Block Codes -- 4.7 A Code Which Corrects Two Errors -- 4.8 Cyclic Codes -- 4.9 Solutions of the Exercises -- Part II Analysis -- 5 Complements in Real and Complex Analysis -- 5.1 Warm-Up Questions and Exercises -- 5.2 Some Known Facts: Bolzano, Rolle, and Cauchy et les autres -- 5.3 Convex and Concave Functions -- 5.4 Stirling's Formula.
5.5 Ordinary Differential Equations -- 5.6 Liouville's Theorem -- 5.7 Multivariable Calculus and Differentials -- 5.8 Optimization -- 5.9 Analytic Functions -- 5.10 Solution of the Exercises -- 6 Complements in Functional Analysis -- 6.1 Topologies and Metric Spaces -- 6.2 Hilbert Spaces -- 6.3 The Lebesgue Space bold upper L 2 left parenthesis double struck upper R comma d t right parenthesisL2(R,dt) -- 6.4 Operators in Banach and Hilbert Space -- 6.5 The Fourier Transform and Distributions -- 6.6 Legendre and Zak -- 6.7 Positive Definite Functions and Kernels -- 6.8 Positive Operators -- 6.9 Reproducing Kernel Hilbert Spaces -- 6.10 Bochner's Theorem -- 6.11 The Fock Space -- 6.12 Hermitian Forms and Reproducing Kernel Krein Spaces -- 6.13 Solutions of the Exercises -- Part III Probability and Applications -- 7 Probability Theory -- 7.1 Review on Finite Probability Spaces -- 7.2 Random Variables in Finite Probability Spaces -- 7.3 Conditional Probabilities -- 7.4 Probability Densities -- 7.5 Sigma-Algebras and General Probability Spaces -- 7.6 Markov Chains -- 7.7 Second-Order Stationary Processes: Discrete Case -- 7.8 Loève's Theorem -- 7.9 Solutions of the Exercises -- 8 Entropy: Discrete Case -- 8.1 Proof of the Source Partition Theorem -- 8.2 Properties of the Entropy -- 8.3 Other Measures of Entropy -- 8.4 Capacity -- 8.5 Metrics on the Set of Random Variables and Entropy -- 8.6 Boltzmann-Gibbs Distribution -- 8.7 Solutions of the Exercises -- 9 Thermodynamics -- 9.1 Thermodynamics -- 9.2 Fluids and the State Equation -- 9.3 The Ideal Gas -- 9.4 Nonideal Gas -- 9.5 Solutions of the Exercises -- References -- Index -- Name Index. |
| Record Nr. | UNINA-9910857794803321 |
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Alpay Daniel
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| Cham : , : Springer International Publishing AG, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Quaternionic de Branges Spaces and Characteristic Operator Function [[electronic resource] /] / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini
| Quaternionic de Branges Spaces and Characteristic Operator Function [[electronic resource] /] / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini |
| Autore | Alpay Daniel |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (X, 116 p. 1 illus.) |
| Disciplina | 512.5 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Functional analysis
Operator theory Functions of complex variables Functional Analysis Operator Theory Functions of a Complex Variable |
| ISBN | 3-030-38312-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Quaternions and matrices -- Slice hyperholomorphic functions -- Rational functions -- Operator models -- Structure theorems for H(A;B) spaces -- J-contractive functions -- The characteristic operator function -- L() spaces and linear fractional transformations -- Canonical differential systems. |
| Record Nr. | UNISA-996418279603316 |
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Alpay Daniel
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Quaternionic de Branges Spaces and Characteristic Operator Function / / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini
| Quaternionic de Branges Spaces and Characteristic Operator Function / / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini |
| Autore | Alpay Daniel |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (X, 116 p. 1 illus.) |
| Disciplina | 512.5 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Functional analysis
Operator theory Functions of complex variables Functional Analysis Operator Theory Functions of a Complex Variable |
| ISBN | 3-030-38312-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preliminaries -- Quaternions and matrices -- Slice hyperholomorphic functions -- Rational functions -- Operator models -- Structure theorems for H(A;B) spaces -- J-contractive functions -- The characteristic operator function -- L() spaces and linear fractional transformations -- Canonical differential systems. |
| Record Nr. | UNINA-9910484245203321 |
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Alpay Daniel
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Slice hyperholomorphic Schur analysis / / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini
| Slice hyperholomorphic Schur analysis / / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini |
| Autore | Alpay Daniel |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 |
| Descrizione fisica | 1 online resource (XII, 362 p.) |
| Disciplina | 515.782 |
| Collana | Operator Theory: Advances and Applications |
| Soggetto topico |
Functions of complex variables
Functional analysis Operator theory Functions of a Complex Variable Functional Analysis Operator Theory |
| ISBN | 3-319-42514-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I: Classical Schur analysis -- Preliminaries -- Rational functions -- Schur analysis -- Part II: Quaternionic analysis -- Finite dimensional preliminaries -- Quaternionic functional analysis -- Slice hyperholomorphic functions -- Slice hyperholomorphic operator-valued functions -- Part III: Quaternionic Schur analysis -- Reproducing kernel spaces and realizations -- Rational slice hyperholomorphic functions -- First applications: scalar interpolation and first order discrete systems -- Interpolation: operator-valued case. |
| Record Nr. | UNINA-9910155444703321 |
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Alpay Daniel
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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