Accession Number : AD0687069

Title :   ON A CLASS OF DIFFERENTIAL EQUATIONS FOR VECTOR-VALUED DISTRIBUTIONS,

Corporate Author : CALIFORNIA UNIV LOS ANGELES

Personal Author(s) : Fattorini,H. O.

Report Date : 1968

Pagination or Media Count : 42

Abstract : The aim of this paper is to seek necessary and sufficient conditions on the linear operator A in a linear topological space in order that the Cauchy problem for the equation (U superscript alpha)-(the product of A and U) = T should be well set in the sense of distributions. Here O < alpha < infinity, U superscript alpha is the fractional derivative of U of order alpha. Such conditions are obtained for alpha integer = or > and then for any alpha > O, this time with the additional assumption of (at most) exponential growth of the solutions at infinity. (Author)

Descriptors :   (*CAUCHY PROBLEM, TOPOLOGY), DIFFERENTIAL EQUATIONS, ANALYTIC FUNCTIONS, OPERATORS(MATHEMATICS), INTEGRAL TRANSFORMS, BANACH SPACE, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE