Clarkson’s inequalities for periodic Sobolev space
| Parent link: | Lobachevskii Journal of Mathematics.— , 1998- Vol. 38, iss. 6.— 2017.— [P. 1146–1155] |
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| Κύριος συγγραφέας: | |
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Περίληψη: | Title screen The validity of Clarkson’s inequalities for periodic functions in the Sobolev space normed without the use of pseudodifferential operators is proved. The norm of a function is defined by using integrals over a fundamental domain of the function and its generalized partial derivatives of all intermediate orders. It is preliminarily shown that Clarkson’s inequalities hold for periodic functions integrable to some power p over a cube of unit measure with identified opposite faces. The work is motivated by the necessity of developing foundations for the functional-analytic approach to evaluating approximation methods. Режим доступа: по договору с организацией-держателем ресурса |
| Γλώσσα: | Αγγλικά |
| Έκδοση: |
2017
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| Θέματα: | |
| Διαθέσιμο Online: | https://doi.org/10.1134/S1995080217060178 |
| Μορφή: | Ηλεκτρονική πηγή Κεφάλαιο βιβλίου |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=657462 |
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| 200 | 1 | |a Clarkson’s inequalities for periodic Sobolev space |f I. V. Korytov | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: p. 1155 (22 tit.)] | ||
| 330 | |a The validity of Clarkson’s inequalities for periodic functions in the Sobolev space normed without the use of pseudodifferential operators is proved. The norm of a function is defined by using integrals over a fundamental domain of the function and its generalized partial derivatives of all intermediate orders. It is preliminarily shown that Clarkson’s inequalities hold for periodic functions integrable to some power p over a cube of unit measure with identified opposite faces. The work is motivated by the necessity of developing foundations for the functional-analytic approach to evaluating approximation methods. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Lobachevskii Journal of Mathematics |d 1998- | ||
| 463 | |t Vol. 38, iss. 6 |v [P. 1146–1155] |d 2017 | ||
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| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a равномерные выпуклости | |
| 610 | 1 | |a единичные сферы | |
| 610 | 1 | |a банахово пространство | |
| 610 | 1 | |a пространство Соболева | |
| 610 | 1 | |a гильбертово пространство | |
| 610 | 1 | |a функциональное пространство | |
| 610 | 1 | |a обратное неравенство Минковского | |
| 610 | 1 | |a неравенства Кларксона | |
| 610 | 1 | |a uniform convexity of the unit sphere | |
| 610 | 1 | |a Banach space | |
| 610 | 1 | |a Sobolev space | |
| 610 | 1 | |a non-Hilbert space | |
| 610 | 1 | |a periodic function space | |
| 610 | 1 | |a inverse Minkowski inequality | |
| 610 | 1 | |a cube of unit measure | |
| 610 | 1 | |a Clarksons inequalities | |
| 700 | 1 | |a Korytov |b I. V. |c mathematician |c Associate Professor of Tomsk Polytechnic University, Candidate of Physical and Mathematical Sciences |f 1961- |g Igor Vitalievich |3 (RuTPU)RU\TPU\pers\37384 |9 20302 | |
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