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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| Дата: | 2001 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/79898 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-79898 |
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dspace |
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irk-123456789-798982015-04-07T03:01:52Z On the averaging procedure over the Cantor set Stanislavsky, A.A. Weron, K. Anomalous diffusion, fractals, and chaos 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. 2001 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/79898 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Anomalous diffusion, fractals, and chaos Anomalous diffusion, fractals, and chaos |
| spellingShingle |
Anomalous diffusion, fractals, and chaos Anomalous diffusion, fractals, and chaos Stanislavsky, A.A. Weron, K. On the averaging procedure over the Cantor set 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. |
| format |
Article |
| author |
Stanislavsky, A.A. Weron, K. |
| author_facet |
Stanislavsky, A.A. Weron, K. |
| author_sort |
Stanislavsky, A.A. |
| title |
On the averaging procedure over the Cantor set |
| 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 |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2001 |
| topic_facet |
Anomalous diffusion, fractals, and chaos |
| url |
http://dspace.nbuv.gov.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. |
| series |
Вопросы атомной науки и техники |
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