Tempered Distributions Supported on a Half-Space of RN and Their Fourier Transforms Academic Article uri icon

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abstract

  • 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.

publication date

  • February 1, 1991