Tempered Distributions Supported on a Half-Space of R<sup>N</sup> and Their Fourier Transforms

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.

Tempered Distributions Supported on a Half-Space of R^N and Their Fourier Transforms Journal Articles