Radial Characteristics Functions.

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)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1973
Accession Number
AD0773603

Entities

People

  • Richard Askey

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Bessel Functions
  • Fourier Transformation
  • Integrals
  • Inverse Problems
  • Mathematical Analysis
  • Mathematics
  • Measure Theory
  • Theorems
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Academic Conference Management
  • Approximation Theory.
  • Calculus or Mathematical Analysis