Refined Spectral Properties of Dirichlet and Neumann Problems for the Laplace Operator in a Rectangular Domain

DOI10.46698/u2067-6110-4876-gOpenAlexW4360612407MaRDI QIDQ6165688

Unnamed Author, Viktor Ivanovich Voĭtitskiĭ

Publication date: 1 August 2023

Published in: Владикавказский математический журнал (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vmj845

zbMATH Keywords

discrete spectrumprime numbersDiophantine approximationspower asymptoticGauss circle problemmultiplicities of eigenvalues

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Quadratic and bilinear Diophantine equations (11D09) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Rate of growth of functions, orders of infinity, slowly varying functions (26A12)

Cites Work

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• Lattice points in planar convex domains
• On the distribution of the number of lattice points inside a family of convex ovals
• On the mean lattice point discrepancy of a convex disc
• On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces
• Primitive lattice points inside an ellipse
• Exponential Sums and Lattice Points III
• Sharp Spectral Asymptotics for Operators with Irregular Coefficients. II. Domains with Boundaries and Degenerations
• Optimal spectral rectangles and lattice ellipses

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