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Tempered Distributions Supported on a Half-Space of RN and Their Fourier Transforms

Published online by Cambridge University Press:  20 November 2018

Jean-Pierre Gabardo
Jean-Pierre Gabardo*
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1
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A fundamental problem in Fourier analysis is to characterize the behaviour of a function (or distribution) whose Fourier transform vanishes in some particular set. Of course, this is, in general, a very difficult question and little seems to be known, except in some special cases. For example, a theorem of Paley-Wiener (Theorem XII in [6]) characterizes exactly the behaviour of the modulus of a function in L2(R) whose Fourier transform vanishes on a half-line.

Keywords

42B1046F10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 1 , 01 February 1991 , pp. 61 - 88
Copyright
Copyright © Canadian Mathematical Society 1991

References

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