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Abel-Tauber theorems for Hankel and Fourier transforms and a problem of Boas
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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