# Accession Number:

## AD0259568

# Title:

## ON ENTIRE FUNCTIONS AND A FOURIER INTEGRAL PROBLEM

# Descriptive Note:

# Corporate Author:

## MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

# Personal Author(s):

# Report Date:

## 1961-07-05

# Pagination or Media Count:

## 1.0

# 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 ax, where ax is some fixed function In some cases, the the question yields easily if we consider ax 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 ax, and the totality of solutions Kx can be displayed, not directly, but through their Fourier transforms, Kx. If, on the other hand, Lp, 1 p 2, existence conditions which involve only ax 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