On a problem in geometry of numbers arising in spectral theory

On a problem in geometry of numbers arising in spectral theory

التفاصيل البيبلوغرافية
Parent link:Russian Journal of Mathematical Physics
Vol. 22, iss. 4.— 2015.— [P. 473-482]
المؤلف الرئيسي: Kordyukov Yu. A. Yuri Arkadievich
مؤلفون آخرون: Yakovlev A. A. Andrey Alexandrovich
الملخص: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
اللغة:الإنجليزية
منشور في: 2015
الموضوعات:
электронный ресурс
труды учёных ТПУ
linear subspace
asymptotic formula
algebraic number
rectangular parallelepiped
adiabatic limit
линейное подпространство
асимптотическая формула
алгебраическое число
прямоугольный параллелепипед
адиабатический предел
الوصول للمادة أونلاين:https://doi.org/10.1134/S106192081504007X
التنسيق: الكتروني فصل الكتاب
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=661579

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