Functions Whose Fourier Transforms Decay at Infinity: An Extension of the Riemann-Lebesgue Lemma

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1972 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 3, pages 485-495 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Bleistein, Norman; Handelsman, Richard A.; Lew, John S.;

doi: 10.1137/0503046

Functions Whose Fourier Transforms Decay at Infinity: An Extension of the Riemann-Lebesgue Lemma

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Abstract

An extension of the Riemann–Lebesgue lemma is stated and proved. We define the space $LL$ of all complex-valued locally integrable functions on $[0, + \infty )$, and the space $RL$ of all functions...

Keywords

Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

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