Harmonic Analysis in Phase Space. (AM-122), Volume 122 / / Gerald B. Folland

• Autore: Folland Gerald B.
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1989
• Descrizione fisica: 1 online resource (289 pages) : illustrations
• Disciplina: 530.1/3
• 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
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• 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
• Sommario/riassunto: This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.
• Titolo autorizzato: Harmonic Analysis in Phase Space. (AM-122), Volume 122
• ISBN: 1-4008-8242-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154752303321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 122.