Про деякi новi критерiї нескiнченної диференцiйовностi перiодичних функцiй
The set of D1 of infinitely differentiable periodic functions is studied in terms of generalized f derivatives defined by a pair f = ( f1, f2) of sequences f1 and f2. It is established that every function F from the set D1 has at least one such derivative whose parameters f1 and f2 decrease faster t...
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| Date: | 2008 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Видавничий дім "Академперіодика" НАН України
2008
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| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/3853 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Про деякi новi критерiї нескiнченної диференцiйовностi перiодичних функцiй / О. I. Степанець, А.С. Сердюк, А.Л. Шидлiч // Доп. НАН України. — 2008. — № 1. — С. 22-26. — Бібліогр.: 3 назв. — укp. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The set of D1 of infinitely differentiable periodic functions is studied in terms of generalized f derivatives defined by a pair f = ( f1, f2) of sequences f1 and f2. It is established that every function F from the set D1 has at least one such derivative whose parameters f1 and f2 decrease faster than any power function. For an arbitrary function from D1 different from a trigonometric polynomial, there exists a pair having the parameters f1 and f2 with the same properties, for which the f derivative already does not exist. On the basis of the proved statements, a number of criteria for a function to belong to the set D1 is given.
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| ISSN: | 1025-6415 |