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    Harmonic Analysis in Phase Space. (AM-122), Volume 122

    Harmonic Analysis in Phase Space. (AM-122), Volume 122

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    Bog E-bog
    • Format
    • Bog, paperback
    • Engelsk

    Beskrivelse

    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.

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  • Vægt425 g
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    10 cm
    book img
    15,2 cm
    22,9 cm

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    Equation Lie-algebra Spectral theory Geometric quantization Number theory Harmonic analysis Symplectic geometry Phase space (Statistical physics) Hermite polynomials Hilbert space Fourier analysis Cauchy-Riemann equations Configuration space Hilbert transform Classical mechanics Bounded operator Quantum harmonic oscillator Stone-Weierstrass Theorem Representation theory Polynomial Hamiltonian mechanics Eigenvalues and Eigenvectors Ordinary differential equation Lie superalgebra Observable Asymptotic expansion Theorem Semigroup Integral transform Phase space Unbounded operator Commutative property State-space Representation Unitary Representation Analytic Continuation Self-adjoint operator Calculation Fourier transform Unitary Operator Partial differential equation Fock space Schroedinger Equation Automorphism Symplectic Group Spectral theorem Heisenberg group Poisson Bracket Quantum-mechanics Fourier integral operator Pseudo-Differential Operator Orthonormal basis Irreducible Representation Hermitian Symmetric Space Antisymmetric tensor Canonical commutation relation Canonical Transformation Gaussian integral Gaussian function Oscillator representation Hamiltonian vector field Projective Hilbert space Siegel disc Translational Symmetry Unit vector Oscillatory integral Phase factor Projection (linear algebra) Wave Packet Symplectic vector space Tangent Vector Unitarity (physics)

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