The number of integer points in a family of anisotropically expanding domains; Monatshefte fur Mathematik; Vol. 178, iss. 1
| Parent link: | Monatshefte fur Mathematik Vol. 178, iss. 1.— 2015.— [P. 97-111] |
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| Hlavní autor: | |
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| Shrnutí: | Title screen We investigate the remainder in the asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space, which remain unchanged along some linear subspace and expand in the directions, orthogonal to this subspace. We prove some estimates for the remainder, imposing additional assumptions on the boundary of the domain. We study the average remainder estimates, where the averages are taken over rotated images of the domain by a subgroup of the group SO(n)SO(n) of orthogonal transformations of the Euclidean space RnRn. Using these results, we improve the remainder estimate in the adiabatic limit formula 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 when 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 |
| Jazyk: | angličtina |
| Vydáno: |
2015
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| Témata: | |
| On-line přístup: | https://doi.org/10.1007/s00605-015-0787-7 |
| Médium: | MixedMaterials Elektronický zdroj Kapitola |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=661580 |
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| 200 | 1 | |a The number of integer points in a family of anisotropically expanding domains |f Yu. A. Kordyukov, A. A. Yakovlev | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 17 tit.] | ||
| 330 | |a We investigate the remainder in the asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space, which remain unchanged along some linear subspace and expand in the directions, orthogonal to this subspace. We prove some estimates for the remainder, imposing additional assumptions on the boundary of the domain. We study the average remainder estimates, where the averages are taken over rotated images of the domain by a subgroup of the group SO(n)SO(n) of orthogonal transformations of the Euclidean space RnRn. Using these results, we improve the remainder estimate in the adiabatic limit formula 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 when 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 Monatshefte fur Mathematik | ||
| 463 | |t Vol. 178, iss. 1 |v [P. 97-111] |d 2015 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a integer points | |
| 610 | 1 | |a anisotropically expanding domains | |
| 610 | 1 | |a convexity | |
| 610 | 1 | |a adiabatic limits | |
| 610 | 1 | |a foliation | |
| 610 | 1 | |a laplace operator | |
| 610 | 1 | |a алгебраическое число | |
| 610 | 1 | |a прямоугольный параллелепипед | |
| 610 | 1 | |a адиабатический предел | |
| 610 | 1 | |a асимптотическая формула 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 | |
| 801 | 2 | |a RU |b 63413507 |c 20200115 |g RCR | |
| 850 | |a 63413507 | ||
| 856 | 4 | |u https://doi.org/10.1007/s00605-015-0787-7 | |
| 942 | |c CF | ||