Accession Number : AD0726034

Title :   Mean-Periodicity in Several Variables.

Descriptive Note : Final technical rept. 1 Feb 70-31 Jan 71,

Corporate Author : MONTPELLIER UNIV (FRANCE) FACULTE DES SCIENCES

Personal Author(s) : Akutowitz,Edwin J.

Report Date : MAY 1971

Pagination or Media Count : 12

Abstract : The author concentrated on extending this theory of mean-periodicity for functions of one variable to functions of several variables. The purpose is to obtain a representation of solution of homogeneous convolution equations through a sum or integral of exponential functions, a sort of extension of the notion of Fourier series. This problem of spectral synthesis, which forms the core of our investigations, is so formulated as to depend upon a sufficiently concrete characterisation Q of a certain quotient space. This problem of characterisation then amounts to proving that a correspondence rho is an isomorphism. But proving the injectivity and surjectivity of rho constitute two exceedingly interesting and far-reaching problems of complex analysis. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, *COMPLEX VARIABLES), FOURIER ANALYSIS, INTEGRAL TRANSFORMS, ANALYTIC FUNCTIONS, FRANCE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE