A simple approach to asymptotic expansions for Fourier integrals of singular functions
type: Item
instance of: scholarly article
title: A simple approach to asymptotic expansions for Fourier integrals of singular functions
zbMATH Open document ID: 1193.42071
author: Avram Sidi
published in: Applied Mathematics and Computation
publication date: 2010-07-19T00:00:00Z
review text: Given the full asymptotic expansions for a Fourier integral \(\int_a^bf(x)e^{\pm isx}dx\) as \(s \to \infty,\) where \(s\) is real positive, \([a,b]\) is a finite interval, and the function \(f(x)\) may have different types of algebraic and logarithmic singularities at \(x=a\) and \(x=b.\) This problem has been treated in the literature by techniques involving neutralizers and Mellin transforms. In this paper, the relevant asymptotic expansions are received by a method that employs more simpler tools.
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 5757605
zbMATH Keywords: Fourier integrals
zbMATH Keywords: Fourier series
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: singular functions
MaRDI profile type: Publication
full work available at URL: j.amc.2010.04.068
OpenAlex ID: W2091342393
cites work: Q3207312
cites work: Q4092387
cites work: Q4059363
cites work: Q3993278
DOI: 10.1016/J.AMC.2010.04.068
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description: scientific article; zbMATH DE number 5757605