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Hardy's Theorem and the Short‐Time Fourier Transform of Schwartz Functions
Author(s) -
Gröchenig Karlheinz,
Zimmermann Georg
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001800
Subject(s) - fourier transform , fourier inversion theorem , fractional fourier transform , wigner distribution function , mathematics , short time fourier transform , distribution (mathematics) , fourier analysis , mathematical analysis , physics , quantum mechanics , quantum
The Schwartz space of rapidly decaying test functions is characterized by the decay of the short‐time Fourier transform or cross‐Wigner distribution. Then a version of Hardy's theorem is proved for the short‐time Fourier transform and for the Wigner distribution.