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Folland G.B. — Harmonic Analysis in Phase Space
Folland G.B. — Harmonic Analysis in Phase Space



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Название: Harmonic Analysis in Phase Space

Автор: Folland G.B.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 277

Добавлена в каталог: 05.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ambiguity function      34
Analytic vector      190
Analytic wave front set      164
Annihilation operator      49
Anti-Wick ordered operator      138
Anti-Wick symbol      138 140
Bargmann kernel      45
Bargmann transform      40
Boson Fock space      48
Calderon — Vaillancourt theorems      122 126
Canonical anticommutation relations      221
Canonical commutation relations      15
Canonical coordinates      12
Canonical transformation      11
Cayley transform      203 242
Centered Gaussian      207
Centered wave packet      144
Characteristic variety      118
Coherent state      30
Conic set      118
Cotlar's lemma      263
Creation operator      49
Elliptic symbol      116
Essential support      118 164
Extended oscillator semigroup      234
FBI transform      160
Fermion Fock space      48
Fock space      40 48
Fourier — Wigner transform      30
Gabor expansion      164
Gabor function      30
Garding's inequality      115 134
Gaussian      207
Groenewold's theorem      197
Group Fourier transform      37
Hamiltonian vector field      11
Harmonic representation      170
Heisenberg group      19 76
Heisenberg group, polarized      19
Heisenberg group, reduced      23
Heisenberg Lie algebra      18
Hermite function      51
Hermite operator      52
Hermite polynomial      52
Hermite semigroup      236
Hudson's theorem      62
Integrated Schroedinger representation      23
Kohn — Nirenberg symbol      93
kq representation      71
Ladder representation      216
Laguerre polynomial      63
Mehler's formula      55
Metaplectic representation      178
Microsupport      118
Moyal bracket      110
Moyal's identity      57
Normalized oscillator semigroup      239
Observable      10 12
Oscillator representation      170
Oscillator semigroup      223
Oscillator semigroup, extended      234
Oscillator semigroup, normalized      239
Phase space      10
Poisson bracket      11
Polarized Heisenberg group      19
Positive operator      129
Principal symbol      102
Pseudolocal operator      113
Quantization      15
Reduced Heisenberg group      23
Representing Function      224
Schroedinger representation      22
Schroedinger representation, integrated      23
Schur's lemma      262
Sharp Garding inequality      134
Siegel disc      203
Siegel half plane      200
Singular support      113
Sobolev space      115
Spin representation      220
Standard Gaussian      207
Stone-von Neumann theorem      35
Subprincipal symbol      102
Symbol      80
Symbol, Kohn — Nirenberg      93
Symbol, principal      102
Symbol, subprincipal      102
Symbol, weyl      80
Symplectic group      11 171
Symplectic Lie algebra      171
Symplectomorphism      11
Theta function      73
Twisted convolution      26
Twisted product      103
Uncertainty principle      27
Van Hove's theorem      199
Wave front set      119 154
Wave front set, analytic      164
Wave packet transform      143 148
Weil — Brezin transform      71
Weyl correspondence      79
Weyl symbol      80
Weyl transform      24
Wick ordered operator      138
Wick symbol      138 139
Wigner distribution      57
Wigner transform      56
Zak transform      71
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