HUSCAP logo Hokkaido Univ. logo

Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >

Abel-Tauber theorems for Hankel and Fourier transforms and a problem of Boas

Files in This Item:
pre436.pdf627.62 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/83582

Title: Abel-Tauber theorems for Hankel and Fourier transforms and a problem of Boas
Authors: Inoue, A. Browse this author
Kikuchi, H. Browse this author
Keywords: Abel-Tauber theorems
Hankel transforms
Fourier transforms
Fourier series
II-variation
Issue Date: 1-Nov-1998
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 436
Start Page: 1
End Page: 20
Abstract: We prove Abel-Tauber theorems for Hankel and Fourier transforms. For example, let f be a locally integrable function on [O, oo) which is eventually decreasing to zero at infinity. Let p = 3, 5, 7, · · · and £ be slowly varying at infinity. We characterize the asymptotic behavior f(t) 􀀕 l(t)t-P as t -+ oo 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69186
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University