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Harmonic Analysis in Phase Space. (AM-122), Volume 122 / / Gerald B. Folland
| Harmonic Analysis in Phase Space. (AM-122), Volume 122 / / Gerald B. Folland |
| Autore | Folland Gerald B. |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (289 pages) : illustrations |
| Disciplina | 530.1/3 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Phase space (Statistical physics)
Harmonic analysis |
| Soggetto non controllato |
Analytic continuation
Analytic function Antisymmetric tensor Asymptotic expansion Automorphism Bilinear form Bounded operator Calculation Canonical commutation relation Canonical transformation Cauchy–Riemann equations Cayley transform Class function (algebra) Classical mechanics Commutative property Complex analysis Configuration space Differential equation Differential geometry Differential operator Eigenvalues and eigenvectors Equation Explicit formula Fock space Fourier analysis Fourier integral operator Fourier transform Functional analysis Gaussian function Gaussian integral Geometric quantization Hamiltonian mechanics Hamiltonian vector field Harmonic analysis Heisenberg group Hermite polynomials Hermitian symmetric space Hilbert space Hilbert transform Integral transform Invariant subspace Irreducible representation Lebesgue measure Lie algebra Lie superalgebra Lie theory Mathematical physics Number theory Observable Ordinary differential equation Orthonormal basis Oscillator representation Oscillatory integral Partial differential equation Phase factor Phase space Point at infinity Poisson bracket Polynomial Power series Probability Projection (linear algebra) Projective Hilbert space Projective representation Projective space Pseudo-differential operator Pullback (category theory) Quadratic function Quantum harmonic oscillator Quantum mechanics Representation theory Schrödinger equation Self-adjoint operator Semigroup Several complex variables Siegel disc Sobolev space Spectral theorem Spectral theory State-space representation Stone's theorem Stone–Weierstrass theorem Summation Symmetric space Symmetric tensor Symplectic geometry Symplectic group Symplectic vector space Symplectomorphism Tangent space Tangent vector Theorem Translational symmetry Unbounded operator Unit vector Unitarity (physics) Unitary operator Unitary representation Variable (mathematics) Wave packet |
| ISBN | 1-4008-8242-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- CONTENTS -- PREFACE -- PROLOGUE. SOME MATTERS OF NOTATION -- CHAPTER 1. THE HEISENBERG GROUP AND ITS REPRESENTATIONS -- CHAPTER 2. QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS -- CHAPTER 3. WAVE PACKETS AND WAVE FRONTS -- CHAPTER 4. THE METAPLECTIC REPRESENTATION -- CHAPTER 5. THE OSCILLATOR SEMIGROUP -- APPENDIX A. GAUSSIAN INTEGRALS AND A LEMMA ON DETERMINANTS -- APPENDIX B. SOME HILBERT SPACE RESULTS -- BIBLIOGRAPHY -- INDEX |
| Record Nr. | UNINA-9910154752303321 |
Folland Gerald B.
|
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hypoelliptic Laplacian and orbital integrals [[electronic resource] /] / Jean-Michel Bismut
| Hypoelliptic Laplacian and orbital integrals [[electronic resource] /] / Jean-Michel Bismut |
| Autore | Bismut Jean-Michel |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2011 |
| Descrizione fisica | 1 online resource (320 p.) |
| Disciplina | 515.7242 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Hypoelliptic
Laplacian operator Definite integrals Orbit method |
| Soggetto genere / forma | Electronic books. |
| Soggetto non controllato |
Bianchi identity
Brownian motion Casimir operator Clifford algebras Clifford variables Dirac operator Euclidean vector space Feynman-Kac formula Gaussian integral Gaussian type estimates Heisenberg algebras Kostant Leftschetz formula Littlewood-Paley decomposition Malliavin calculus Pontryagin maximum principle Selberg's trace formula Sobolev spaces Toponogov's theorem Witten complex action functional complexification conjugations convergence convexity de Rham complex displacement function distance function elliptic Laplacian elliptic orbital integrals fixed point formulas flat bundle general kernels general orbital integrals geodesic flow geodesics harmonic oscillator heat kernel heat kernels heat operators hypoelliptic Laplacian hypoelliptic deformation hypoelliptic heat kernel hypoelliptic heat kernels hypoelliptic operators hypoelliptic orbital integrals index formulas index theory infinite dimensional orbital integrals keat kernels local index theory locally symmetric space matrix part model operator nondegeneracy orbifolds orbital integrals parallel transport trivialization probabilistic construction pseudodistances quantitative estimates quartic term real vector space refined estimates rescaled heat kernel resolvents return map rough estimates scalar heat kernel scalar heat kernels scalar hypoelliptic Laplacian scalar hypoelliptic heat kernels scalar hypoelliptic operator scalar part semisimple orbital integrals smooth kernels standard elliptic heat kernel supertraces symmetric space symplectic vector space trace formula unbounded operators uniform bounds uniform estimates variational problems vector bundles wave equation wave kernel wave operator |
| ISBN |
1-283-16387-X
9786613163875 1-4008-4057-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Acknowledgments -- Introduction -- Chapter One. Clifford and Heisenberg algebras -- Chapter Two. The hypoelliptic Laplacian on X = G/K -- Chapter Three. The displacement function and the return map -- Chapter Four. Elliptic and hypoelliptic orbital integrals -- Chapter Five. Evaluation of supertraces for a model operator -- Chapter Six. A formula for semisimple orbital integrals -- Chapter Seven. An application to local index theory -- Chapter Eight. The case where [k (γ) ; p0] = 0 -- Chapter Nine. A proof of the main identity -- Chapter Ten. The action functional and the harmonic oscillator -- Chapter Eleven. The analysis of the hypoelliptic Laplacian -- Chapter Twelve. Rough estimates on the scalar heat kernel -- Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b -- Chapter Fourteen. The heat kernel qXb;t for bounded b -- Chapter Fifteen. The heat kernel qXb;t for b large -- Bibliography -- Subject Index -- Index of Notation |
| Record Nr. | UNINA-9910456831103321 |
|
Bismut Jean-Michel
|
||
| Princeton, : Princeton University Press, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hypoelliptic Laplacian and orbital integrals [[electronic resource] /] / Jean-Michel Bismut
| Hypoelliptic Laplacian and orbital integrals [[electronic resource] /] / Jean-Michel Bismut |
| Autore | Bismut Jean-Michel |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2011 |
| Descrizione fisica | 1 online resource (320 p.) |
| Disciplina | 515.7242 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Hypoelliptic
Laplacian operator Definite integrals Orbit method |
| Soggetto non controllato |
Bianchi identity
Brownian motion Casimir operator Clifford algebras Clifford variables Dirac operator Euclidean vector space Feynman-Kac formula Gaussian integral Gaussian type estimates Heisenberg algebras Kostant Leftschetz formula Littlewood-Paley decomposition Malliavin calculus Pontryagin maximum principle Selberg's trace formula Sobolev spaces Toponogov's theorem Witten complex action functional complexification conjugations convergence convexity de Rham complex displacement function distance function elliptic Laplacian elliptic orbital integrals fixed point formulas flat bundle general kernels general orbital integrals geodesic flow geodesics harmonic oscillator heat kernel heat kernels heat operators hypoelliptic Laplacian hypoelliptic deformation hypoelliptic heat kernel hypoelliptic heat kernels hypoelliptic operators hypoelliptic orbital integrals index formulas index theory infinite dimensional orbital integrals keat kernels local index theory locally symmetric space matrix part model operator nondegeneracy orbifolds orbital integrals parallel transport trivialization probabilistic construction pseudodistances quantitative estimates quartic term real vector space refined estimates rescaled heat kernel resolvents return map rough estimates scalar heat kernel scalar heat kernels scalar hypoelliptic Laplacian scalar hypoelliptic heat kernels scalar hypoelliptic operator scalar part semisimple orbital integrals smooth kernels standard elliptic heat kernel supertraces symmetric space symplectic vector space trace formula unbounded operators uniform bounds uniform estimates variational problems vector bundles wave equation wave kernel wave operator |
| ISBN |
1-283-16387-X
9786613163875 1-4008-4057-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Acknowledgments -- Introduction -- Chapter One. Clifford and Heisenberg algebras -- Chapter Two. The hypoelliptic Laplacian on X = G/K -- Chapter Three. The displacement function and the return map -- Chapter Four. Elliptic and hypoelliptic orbital integrals -- Chapter Five. Evaluation of supertraces for a model operator -- Chapter Six. A formula for semisimple orbital integrals -- Chapter Seven. An application to local index theory -- Chapter Eight. The case where [k (γ) ; p0] = 0 -- Chapter Nine. A proof of the main identity -- Chapter Ten. The action functional and the harmonic oscillator -- Chapter Eleven. The analysis of the hypoelliptic Laplacian -- Chapter Twelve. Rough estimates on the scalar heat kernel -- Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b -- Chapter Fourteen. The heat kernel qXb;t for bounded b -- Chapter Fifteen. The heat kernel qXb;t for b large -- Bibliography -- Subject Index -- Index of Notation |
| Record Nr. | UNINA-9910781482503321 |
|
Bismut Jean-Michel
|
||
| Princeton, : Princeton University Press, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hypoelliptic Laplacian and orbital integrals [[electronic resource] /] / Jean-Michel Bismut
| Hypoelliptic Laplacian and orbital integrals [[electronic resource] /] / Jean-Michel Bismut |
| Autore | Bismut Jean-Michel |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2011 |
| Descrizione fisica | 1 online resource (320 p.) |
| Disciplina | 515.7242 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Hypoelliptic
Laplacian operator Definite integrals Orbit method |
| Soggetto non controllato |
Bianchi identity
Brownian motion Casimir operator Clifford algebras Clifford variables Dirac operator Euclidean vector space Feynman-Kac formula Gaussian integral Gaussian type estimates Heisenberg algebras Kostant Leftschetz formula Littlewood-Paley decomposition Malliavin calculus Pontryagin maximum principle Selberg's trace formula Sobolev spaces Toponogov's theorem Witten complex action functional complexification conjugations convergence convexity de Rham complex displacement function distance function elliptic Laplacian elliptic orbital integrals fixed point formulas flat bundle general kernels general orbital integrals geodesic flow geodesics harmonic oscillator heat kernel heat kernels heat operators hypoelliptic Laplacian hypoelliptic deformation hypoelliptic heat kernel hypoelliptic heat kernels hypoelliptic operators hypoelliptic orbital integrals index formulas index theory infinite dimensional orbital integrals keat kernels local index theory locally symmetric space matrix part model operator nondegeneracy orbifolds orbital integrals parallel transport trivialization probabilistic construction pseudodistances quantitative estimates quartic term real vector space refined estimates rescaled heat kernel resolvents return map rough estimates scalar heat kernel scalar heat kernels scalar hypoelliptic Laplacian scalar hypoelliptic heat kernels scalar hypoelliptic operator scalar part semisimple orbital integrals smooth kernels standard elliptic heat kernel supertraces symmetric space symplectic vector space trace formula unbounded operators uniform bounds uniform estimates variational problems vector bundles wave equation wave kernel wave operator |
| ISBN |
1-283-16387-X
9786613163875 1-4008-4057-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Acknowledgments -- Introduction -- Chapter One. Clifford and Heisenberg algebras -- Chapter Two. The hypoelliptic Laplacian on X = G/K -- Chapter Three. The displacement function and the return map -- Chapter Four. Elliptic and hypoelliptic orbital integrals -- Chapter Five. Evaluation of supertraces for a model operator -- Chapter Six. A formula for semisimple orbital integrals -- Chapter Seven. An application to local index theory -- Chapter Eight. The case where [k (γ) ; p0] = 0 -- Chapter Nine. A proof of the main identity -- Chapter Ten. The action functional and the harmonic oscillator -- Chapter Eleven. The analysis of the hypoelliptic Laplacian -- Chapter Twelve. Rough estimates on the scalar heat kernel -- Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b -- Chapter Fourteen. The heat kernel qXb;t for bounded b -- Chapter Fifteen. The heat kernel qXb;t for b large -- Bibliography -- Subject Index -- Index of Notation |
| Record Nr. | UNINA-9910827349603321 |
|
Bismut Jean-Michel
|
||
| Princeton, : Princeton University Press, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||