Accession Number : AD0700419

Title :   REPRESENTATION OF FUNCTIONS BY ORTHOGONAL SERIES.

Descriptive Note : R. E. Gibson Library bulletin translation series,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Osipov,R. I.

Report Date : 31 OCT 1969

Pagination or Media Count : 22

Abstract : The author proves the following theorem on the basis of a direct construction of the functions (phi sub n)(x). Let summation from n=1 to n=infinity of ((a sub n)squared)= + infinity and let F(x) be an arbitrary measurable function, with extended real values, on (0,1). Then there exists an orthonormal system (phi sub n)(x) with the property that each rearrangement of the series summation of ((a sub n)(phi sub n)(x)) converges almost everywhere to F(x). (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), APPROXIMATION(MATHEMATICS)), (*SERIES(MATHEMATICS), CONVERGENCE), FOURIER ANALYSIS, POLYNOMIALS, THEOREMS, USSR

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE