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

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)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1971
Accession Number
AD0722681

Entities

People

  • Norman Bleistein
  • Richard A. Handelsman

Organizations

  • Denver Research Institute

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Mathematics
  • Sequences
  • Sequences (Mathematics)

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.