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Abel-Tauber theorems for Hankel and Fourier transforms
| Title: | Abel-Tauber theorems for Hankel and Fourier transforms |
| Other Titles: | ハンケル変換とフーリエ変換に対するアーベル・タウバー型定理について |
| Authors: | Kikuchi, Hideyuki1 Browse this author |
| Authors(alt): | 菊地, 秀行1 |
| Issue Date: | 25-Mar-1999 |
| Publisher: | Hokkaido University |
| Abstract: | We prove Abel-Tauber theorems for Hankel and Fourier transforms. For example, let f be a locally integrable function on [0,∞) which is eventually decreasing to zero at infinity. Let ρ = 3, 5, 7, … and ℓ be slowly varying at infinity. We characterize the asymptotic behavior f(t) ∼ ℓ(t)t-ρ as t → ∞ in terrns of the Fourier cosine transform of f. Similar results for sine and Hankel transforms are also obtained. As an application, we can give an answer to a problem of R. P. Boas on Fourier series. |
| Conffering University: | 北海道大学 |
| Degree Report Number: | 甲第4600号 |
| Degree Level: | 博士 |
| Degree Discipline: | 理学 |
| Type: | theses (doctoral) |
| URI: | http://hdl.handle.net/2115/51577 |
| Appears in Collections: | 学位論文 (Theses) > 博士 （理学）
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Submitter: 菊地 秀行
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