Accession Number : AD0722681

Title :   Functions Whose Fourier Transform Decays at Infinity; An Extension of the Riemann Lebesgue Lemma,

Corporate Author : DENVER RESEARCH INST COLO DIV OF MATHEMATICAL SCIENCES

Personal Author(s) : Bleistein,Norman ; Handelsman,Richard A.

Report Date : APR 1971

Pagination or Media Count : 13

Abstract : An extension of the Riemann Lebesgue Lemma is stated and proved. The class of functions considered are locally L sub 1 on (0, infinity) and have asymptotic expansion as t approaches infinity of the form f(t) is approximately equal to exp(i alpha (t sup nu)). Summation, n=0 to infinity, summation m=0 to N(m) of ((C sub mn)(t sup(r sub m))((log t) to the nth power). Here the sequence (Re r sub m) increases monotonically to plus infinity, Re r sub 0 > 0 and N(m) is finite for each m. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), ASYMPTOTIC SERIES), (*INTEGRAL TRANSFORMS, CONVERGENCE), FOURIER ANALYSIS, NUMERICAL INTEGRATION, CONVERGENCE

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE