The problem of the number of integer points in families of anisotropically expanding domains, with applications to spectral theory

DOI10.1134/S0001434612090295zbMath1290.11133OpenAlexW2082692798MaRDI QIDQ1929799

Andrey A. Yakovlev, Yurii A. Kordyukov

Publication date: 9 January 2013

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434612090295

zbMATH Keywords

asymptoticsspectral asymptoticsadiabatic limitmagnetic Schrödinger operatornumber of integer pointsaverage remainder estimate

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 (3)

Eigenvalue Optimisation on Flat Tori and Lattice Points in Anisotropically Expanding Domains ⋮ 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

• Unnamed Item
• Complete biorthogonal systems in Banach spaces
• Sharp rate of average decay of the Fourier transform of a bounded set

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