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Gerald B. Folland

Harmonic Analysis in Phase Space

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€107.99
A01=Gerald B. Folland
Analytic continuation
Antisymmetric tensor
Asymptotic expansion
Author_Gerald B. Folland
Automorphism
Bounded operator
Calculation
Canonical commutation relation
Canonical transformation
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Category=PHS
Cauchy-Riemann equations
Classical mechanics
Commutative property
Configuration space
Eigenvalues and eigenvectors
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Equation
Fock space
Fourier analysis
Fourier integral operator
Fourier transform
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
Irreducible representation
Lie algebra
Lie superalgebra
Number theory
Observable
Ordinary differential equation
Orthonormal basis
Oscillator representation
Oscillatory integral
Partial differential equation
Phase factor
Phase space
Poisson bracket
Polynomial
Projection (linear algebra)
Projective Hilbert space
Pseudo-differential operator
Quantum harmonic oscillator
Quantum mechanics
Representation theory
Schrodinger equation
Self-adjoint operator
Semigroup
Siegel disc
Spectral theorem
Spectral theory
State-space representation
Stone-Weierstrass theorem
Symplectic geometry
Symplectic group
Symplectic vector space
Tangent vector
Theorem
Translational symmetry
Unbounded operator
Unit vector
Unitarity (physics)
Unitary operator
Unitary representation
Wave packet

Product details

  • ISBN 9780691085289
  • Weight: 425g
  • Dimensions: 152 x 229mm
  • Publication Date: 21 Mar 1989
  • Publisher: Princeton University Press
  • Publication City/Country: US
  • Product Form: Paperback
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Description
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.