Integer points in domains and adiabatic limits; St. Petersburg Mathematical Journal; Vol. 23, iss. 6
| Parent link: | St. Petersburg Mathematical Journal Vol. 23, iss. 6.— 2012.— [P. 977-987] |
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| Hovedforfatter: | |
| Andre forfattere: | |
| Summary: | Title screen An asymptotic formula is proved for the number of integral points in a family of bounded domains with smooth boundary in Euclidean space; these domains remain unchanged along some linear subspace and expand in the directions orthogonal to this subspace. A sharper estimate for the remainder is obtained in the case where the domains are strictly convex. These results make it possible to improve the remainder estimate in the adiabatic limit formula (due to the first author) for the eigenvalue distribution function of the Laplace operator associated with a bundle-like metric on a compact manifold equipped with a Riemannian foliation in the particular case where the foliation is a linear foliation on the torus and the metric is the standard Euclidean metric on the torus. Режим доступа: по договору с организацией-держателем ресурса |
| Sprog: | engelsk |
| Udgivet: |
2012
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| Fag: | |
| Online adgang: | https://doi.org/10.1090/S1061-0022-2012-01225-2 |
| Format: | MixedMaterials Electronisk Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=661583 |
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| 200 | 1 | |a Integer points in domains and adiabatic limits |f Yu. A. Kordyukov, A. A. Yakovlev | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 16 tit.] | ||
| 330 | |a An asymptotic formula is proved for the number of integral points in a family of bounded domains with smooth boundary in Euclidean space; these domains remain unchanged along some linear subspace and expand in the directions orthogonal to this subspace. A sharper estimate for the remainder is obtained in the case where the domains are strictly convex. These results make it possible to improve the remainder estimate in the adiabatic limit formula (due to the first author) for the eigenvalue distribution function of the Laplace operator associated with a bundle-like metric on a compact manifold equipped with a Riemannian foliation in the particular case where the foliation is a linear foliation on the torus and the metric is the standard Euclidean metric on the torus. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t St. Petersburg Mathematical Journal | ||
| 463 | |t Vol. 23, iss. 6 |v [P. 977-987] |d 2012 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a Integer points | |
| 610 | 1 | |a lattices | |
| 610 | 1 | |a domains | |
| 610 | 1 | |a convexity | |
| 610 | 1 | |a adiabatic limits | |
| 610 | 1 | |a foliation | |
| 610 | 1 | |a Laplace operator | |
| 610 | 1 | |a адиабатические пределы | |
| 610 | 1 | |a оператор Лапласа | |
| 700 | 1 | |a Kordyukov |b Yu. A. |g Yuri Arkadievich | |
| 701 | 1 | |a Yakovlev |b A. A. |c specialist in the field of petroleum engineering |c First Vice-Rector, Associate Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1981- |g Andrey Alexandrovich |3 (RuTPU)RU\TPU\pers\45819 | |
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| 856 | 4 | |u https://doi.org/10.1090/S1061-0022-2012-01225-2 | |
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