Abel-Tauber theorems for Hankel and Fourier transforms and a problem of Boas
type: Item
instance of: scholarly article
title: Abel-Tauber theorems for Hankel and Fourier transforms and a problem of Boas
zbMATH Open document ID: 0939.40003
author: Hideyuki Kikuchi
author: Akihiko Inoue
published in: Hokkaido Mathematical Journal
publication date: 2000-01-31T00:00:00Z
review text: The authors prove five interesting theorems on the subject determined by the title of the paper. A more specified characterization of the results is given in the abstract as follows: We prove Abel-Tauber theorems for Hankel and Fourier transforms. For example, let \(f\) be a locally integrable function on \([0,\infty)\) which is eventually decreasing to zero at infinity. Let \(\rho= 3, 5, 7, \dots\) and \(\ell\) be slowly varying at infinity. We characterize the asymptotic behavior \(f(t) \sim \ell(t)t^{-\rho}\) as \(t\to \infty\) in terms of the Fourier cosine transform of \(f\). Similar results for sine and Hankel transforms are also obtained. As an application, we give an answer to a problem of R. P. Boas on Fourier series.
Mathematics Subject Classification ID: 40E05
Mathematics Subject Classification ID: 42A16
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 1396101
zbMATH Keywords: problem of Boas
zbMATH Keywords: Abel-Tauber theorems
zbMATH Keywords: Hankel and Fourier transforms
zbMATH Keywords: Fourier cosine transform
zbMATH Keywords: Fourier series
reviewed by: László Leindler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351001238
OpenAlex ID: W2073351015
DOI: 10.14492/HOKMJ/1351001238
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description: scientific article; zbMATH DE number 1396101