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Three-Term Asymptotics of the Spectrum of Self-Similar Fractal Drums
http://hdl.handle.net/2261/1247
http://hdl.handle.net/2261/12471f25bbf6-ee01-42d1-8a7a-f0145f6496e6
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms060106.pdf (256.5 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2008-03-04 | |||||
| タイトル | ||||||
| タイトル | Three-Term Asymptotics of the Spectrum of Self-Similar Fractal Drums | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Gerling, Jurgen
× Gerling, Jurgen |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | In the present paper we consider the number $\cN_\Om(\la)$ of eigenvalues not exceeding $\la$ of the negative Laplacian with homogeneous {\sc Dirichlet} boundary conditions in a domain $\Om\subset\RR^n$ with fractal boundary $\partial \Om$. It is known that for $\la\to\infty$, $\cN_\Om(\la)=\cC_n|\Om|_n\la^{n/2}+O(\la^{D/2})$, where $D$ is the {\sc Minkowski} dimension of $\partial\Om$. For a certain class of domains with self--similar boundary, so-called ""fractal drums"", we obtain a second term of the form $-\cF(\ln\la)\,\la^{D/2}$ with a bounded periodic function $\cF$ and a third term. We investigate the function $\cF$ which contains a generalized {\sc Weierstrass} function with a self--similar fractal graph. Exact estimates for the {\sc Minkowski} dimension for this graph will be presented. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 6, 号 1, p. 101-126, 発行日 1999 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| フォーマット | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | application/pdf | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR1683321 | ||||||
| Mathmatical Subject Classification | ||||||
| 35P20(MSC1991) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 1997-11-21 | ||||||
