Accession Number : AD0259568

Title :   ON ENTIRE FUNCTIONS AND A FOURIER INTEGRAL PROBLEM

Corporate Author : MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

Personal Author(s) : SHEEHAN,J.A.

Report Date : 05 JUL 1961

Pagination or Media Count : 1

Abstract : Some previous work of Akutowicz on the following problem is given: that (x),( L2), is null outside some finite interval, what can be said about , if it is known that its Fourier transform, , satisfies (x) = a(x), where a(x) is some fixed function In some cases, the the question yields easily if we consider a(x) 2, which is readily seen to be continuable as a function of exponential type. Specifically, if Lp, (p > 2), the problem is tractable in the sense that it always has a solution (subject to simple conditions on a(x), and the totality of solutions K(x) can be displayed, not directly, but through their Fourier transforms, K(x). If, on the other hand, Lp, (1 < p < 2), existence conditions which involve only a(x) do not appear, and we find it necessary to augment the hypotheses. Even with augmented hypotheses, the conclusions are substantially weaker than in the case p > 2. (Author)

Descriptors :   *INTEGRAL TRANSFORMS, FUNCTIONS(MATHEMATICS), INTEGRAL EQUATIONS, POLYNOMIALS

Distribution Statement : APPROVED FOR PUBLIC RELEASE