On the averaging procedure over the Cantor set
The procedure of averaging a smooth function over the normalized density of the Cantor set (A. Le Mehaute, R.R. Nigmatullin, L. Nivanen. Fleches du temps et geometric fractale. Paris: “Hermes”, 1998, Chapter 5) has been shown not to reduce exactly the convolution to the classical fractional integral...
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| Veröffentlicht in: | Вопросы атомной науки и техники |
|---|---|
| Datum: | 2001 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/79898 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the averaging procedure over the Cantor set / A.A. Stanislavsky, K. Weron // Вопросы атомной науки и техники. — 2001. — № 6. — С. 245-246. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862703470061027328 |
|---|---|
| author | Stanislavsky, A.A. Weron, K. |
| author_facet | Stanislavsky, A.A. Weron, K. |
| citation_txt | On the averaging procedure over the Cantor set / A.A. Stanislavsky, K. Weron // Вопросы атомной науки и техники. — 2001. — № 6. — С. 245-246. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The procedure of averaging a smooth function over the normalized density of the Cantor set (A. Le Mehaute, R.R. Nigmatullin, L. Nivanen. Fleches du temps et geometric fractale. Paris: “Hermes”, 1998, Chapter 5) has been shown not to reduce exactly the convolution to the classical fractional integral of Riemann-Liouville type. Although the asymptotic behavior of the self-similar convolution kernel is very close to the product of a power and a log-periodic function, this is not obviously enough to claim the direct relationship between the fractals and the fractional calculus.
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| first_indexed | 2025-12-07T16:47:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-79898 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:47:53Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Stanislavsky, A.A. Weron, K. 2015-04-06T16:39:40Z 2015-04-06T16:39:40Z 2001 On the averaging procedure over the Cantor set / A.A. Stanislavsky, K. Weron // Вопросы атомной науки и техники. — 2001. — № 6. — С. 245-246. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 05.40.-a, 05.45.-a, 05.46.-k. https://nasplib.isofts.kiev.ua/handle/123456789/79898 The procedure of averaging a smooth function over the normalized density of the Cantor set (A. Le Mehaute, R.R. Nigmatullin, L. Nivanen. Fleches du temps et geometric fractale. Paris: “Hermes”, 1998, Chapter 5) has been shown not to reduce exactly the convolution to the classical fractional integral of Riemann-Liouville type. Although the asymptotic behavior of the self-similar convolution kernel is very close to the product of a power and a log-periodic function, this is not obviously enough to claim the direct relationship between the fractals and the fractional calculus. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Anomalous diffusion, fractals, and chaos On the averaging procedure over the Cantor set О процедуре усреднения по множеству Кантора Article published earlier |
| spellingShingle | On the averaging procedure over the Cantor set Stanislavsky, A.A. Weron, K. Anomalous diffusion, fractals, and chaos |
| title | On the averaging procedure over the Cantor set |
| title_alt | О процедуре усреднения по множеству Кантора |
| title_full | On the averaging procedure over the Cantor set |
| title_fullStr | On the averaging procedure over the Cantor set |
| title_full_unstemmed | On the averaging procedure over the Cantor set |
| title_short | On the averaging procedure over the Cantor set |
| title_sort | on the averaging procedure over the cantor set |
| topic | Anomalous diffusion, fractals, and chaos |
| topic_facet | Anomalous diffusion, fractals, and chaos |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79898 |
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