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: | English |
| Veröffentlicht: |
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| id |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the averaging procedure over the Cantor set |
| spellingShingle |
On the averaging procedure over the Cantor set Stanislavsky, A.A. Weron, K. Anomalous diffusion, fractals, and chaos |
| title_short |
On the averaging procedure over the Cantor set |
| 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_sort |
on the averaging procedure over the cantor set |
| author |
Stanislavsky, A.A. Weron, K. |
| author_facet |
Stanislavsky, A.A. Weron, K. |
| topic |
Anomalous diffusion, fractals, and chaos |
| topic_facet |
Anomalous diffusion, fractals, and chaos |
| publishDate |
2001 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
О процедуре усреднения по множеству Кантора |
| 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.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/79898 |
| 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. |
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| first_indexed |
2025-12-07T16:47:53Z |
| last_indexed |
2025-12-07T16:47:53Z |
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