
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 ;MRCTSR1262DA31124ARO(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 ndimensions is presented. (Modified author abstract)
Descriptors : *FOURIER TRANSFORMATION, MEASURE THEORY, BESSEL FUNCTIONS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE