On a problem in geometry of numbers arising in spectral theory; Russian Journal of Mathematical Physics; Vol. 22, iss. 4
| Parent link: | Russian Journal of Mathematical Physics Vol. 22, iss. 4.— 2015.— [P. 473-482] |
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| Main Author: | |
| Other Authors: | |
| Summary: | Title screen We study the lattice point counting problem for a class of families of domains in a Euclidean space. This class consists of anisotropically expanding bounded domains that remain unchanged along some fixed linear subspace and expand in directions orthogonal to this subspace. We find the leading term in the asymptotics of the number of lattice points in such family of domains and prove remainder estimates in this asymptotics under various conditions on the lattice and the family of domains. As a consequence, we prove an asymptotic formula for the eigenvalue distribution function of the Laplace operator on a flat torus in adiabatic limit determined by a linear foliation with a nontrivial remainder estimate. Режим доступа: по договору с организацией-держателем ресурса |
| Language: | English |
| Published: |
2015
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| Subjects: | |
| Online Access: | https://doi.org/10.1134/S106192081504007X |
| Format: | MixedMaterials Electronic Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=661579 |
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| 200 | 1 | |a On a problem in geometry of numbers arising in spectral theory |f Yu. A. Kordyukov, A. A. Yakovlev | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 11 tit.] | ||
| 330 | |a We study the lattice point counting problem for a class of families of domains in a Euclidean space. This class consists of anisotropically expanding bounded domains that remain unchanged along some fixed linear subspace and expand in directions orthogonal to this subspace. We find the leading term in the asymptotics of the number of lattice points in such family of domains and prove remainder estimates in this asymptotics under various conditions on the lattice and the family of domains. As a consequence, we prove an asymptotic formula for the eigenvalue distribution function of the Laplace operator on a flat torus in adiabatic limit determined by a linear foliation with a nontrivial remainder estimate. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Russian Journal of Mathematical Physics | ||
| 463 | |t Vol. 22, iss. 4 |v [P. 473-482] |d 2015 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a linear subspace | |
| 610 | 1 | |a asymptotic formula | |
| 610 | 1 | |a algebraic number | |
| 610 | 1 | |a rectangular parallelepiped | |
| 610 | 1 | |a adiabatic limit | |
| 610 | 1 | |a линейное подпространство | |
| 610 | 1 | |a асимптотическая формула | |
| 610 | 1 | |a алгебраическое число | |
| 610 | 1 | |a прямоугольный параллелепипед | |
| 610 | 1 | |a адиабатический предел | |
| 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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