Integer points in domains and adiabatic limits

DOI10.1090/S1061-0022-2012-01225-2zbMath1290.11134arXiv1006.4977MaRDI QIDQ2849079

Andrey A. Yakovlev, Yurii A. Kordyukov

Publication date: 16 September 2013

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.4977

zbMATH Keywords

domainsconvexityLaplace operatorfoliationlatticesinteger pointsadiabatic limits

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Eigenvalue problems for linear operators (47A75) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Lattice points in specified regions (11P21) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (2)

The number of integer points in a family of anisotropically expanding domains ⋮ On a problem in geometry of numbers arising in spectral theory

Cites Work

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• Adiabatic limits and spectral geometry of foliations
• Nombre de points entiers dans une famille homothétique de domaines de ${R}$
• Semiclassical Spectral Asymptotics on Foliated Manifolds
• A Lattice-Point Problem
• A Lattice-Point Problem. II

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