| 000 | 02731nlm1a2200445 4500 | ||
|---|---|---|---|
| 001 | 661580 | ||
| 005 | 20231030041751.0 | ||
| 035 | _a(RuTPU)RU\TPU\network\32220 | ||
| 035 | _aRU\TPU\network\32219 | ||
| 090 | _a661580 | ||
| 100 | _a20200115a2015 k y0engy50 ba | ||
| 101 | 0 | _aeng | |
| 135 | _adrcn ---uucaa | ||
| 181 | 0 | _ai | |
| 182 | 0 | _ab | |
| 200 | 1 |
_aThe number of integer points in a family of anisotropically expanding domains _fYu. A. Kordyukov, A. A. Yakovlev |
|
| 203 |
_aText _celectronic |
||
| 300 | _aTitle screen | ||
| 320 | _a[References: 17 tit.] | ||
| 330 | _aWe 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 | _aРежим доступа: по договору с организацией-держателем ресурса | ||
| 461 | _tMonatshefte fur Mathematik | ||
| 463 |
_tVol. 178, iss. 1 _v[P. 97-111] _d2015 |
||
| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 610 | 1 | _ainteger points | |
| 610 | 1 | _aanisotropically expanding domains | |
| 610 | 1 | _aconvexity | |
| 610 | 1 | _aadiabatic limits | |
| 610 | 1 | _afoliation | |
| 610 | 1 | _alaplace operator | |
| 610 | 1 | _aалгебраическое число | |
| 610 | 1 | _aпрямоугольный параллелепипед | |
| 610 | 1 | _aадиабатический предел | |
| 610 | 1 | _aасимптотическая формула Лапласа | |
| 700 | 1 |
_aKordyukov _bYu. A. _gYuri Arkadievich |
|
| 701 | 1 |
_aYakovlev _bA. A. _cspecialist in the field of petroleum engineering _cFirst Vice-Rector, Associate Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences _f1981- _gAndrey Alexandrovich _2stltpush _3(RuTPU)RU\TPU\pers\45819 |
|
| 801 | 2 |
_aRU _b63413507 _c20200115 _gRCR |
|
| 856 | 4 | _uhttps://doi.org/10.1007/s00605-015-0787-7 | |
| 942 | _cCF | ||