Accession Number : AD0773603

Title :   Radial Characteristics Functions.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Askey,Richard

Report Date : NOV 1973

Pagination or Media Count : 20

Abstract : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTERRadial Characteristics Functions.Technical summary rept.,SAskey,Richard ;MRC-TSR-1262DA-31-124-ARO(D)-462*Fourier transformation, Measure theory, Bessel functions, TheoremsPolya theorem, *Characteristic functionsIn 1918 Polya proved that the Fourier transform of an even function which is convex for x = or > 0, continuous and vanishes at infinity is nonnegative. In 1949 he pointed out that this transform could be inverted, so that the function is positive definite, and if it is one when x is zero, it is a characteristic function. An extension of this result to n-dimensions is presented. (Modified author abstract)

Descriptors :   *FOURIER TRANSFORMATION, MEASURE THEORY, BESSEL FUNCTIONS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE