Accession Number : AD0673550

Title :   THE ANALYTICITY OF SOLUTIONS OF SINGULAR INTEGRAL EQUATIONS.

Descriptive Note : Technical rept.,

Corporate Author : MINNESOTA UNIV MINNEAPOLIS SCHOOL OF MATHEMATICS

Personal Author(s) : Kahane,Charles S.

Report Date : JUL 1968

Pagination or Media Count : 68

Abstract : The author studies the analyticity properties of solutions of the equation g = Kf where K is a singular integral operator of the Calderon-Zygmund type with g and f in L sub p. Assuming that g and K are locally analytic in a suitable sense and that the symbol of the operator K is locally not equal to 0, any solution of the equation g = Kf is shown to be locally analytic. This generalizes the well-known result that solutions of linear analytic elliptic partial differential equations are themselves analytic. (Author)

Descriptors :   (*INTEGRAL EQUATIONS, ANALYTIC FUNCTIONS), OPERATORS(MATHEMATICS), COMPLEX VARIABLES, SPECIAL FUNCTIONS(MATHEMATICAL), POTENTIAL THEORY, PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL TRANSFORMS, FOURIER ANALYSIS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE