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A Generalization of the Theorem of Hardy: A Most General Version of the Uncertainty Principle for Fourier Integrals
Author(s) -
Pfannschmidt Christian
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961820114
Subject(s) - mathematics , generalization , fourier inversion theorem , fourier transform , assertion , hardy space , pure mathematics , function (biology) , uncertainty principle , mathematical analysis , calculus (dental) , algebra over a field , fourier analysis , short time fourier transform , medicine , physics , dentistry , quantum mechanics , evolutionary biology , computer science , quantum , biology , programming language
N. Wiener remarked that a non ‐ identically vanishing real function and its Fourier transform cannot both decay “very fast”. It was Hardy who specified and proved this assertion in 1933. In the present paper Hardy's theorem will be generalized. Moreover, it will be shown that further weakening of these assumptions does not make sense.