Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction

DOI10.1134/S0081543819040047zbMath1430.35169OpenAlexW2980686998MaRDI QIDQ2284196

Denis I. Borisov

Publication date: 14 January 2020

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543819040047

zbMATH Keywords

band spectrumLaplacianperiodic operatorBethe-Sommerfeld conjectureabsence of gapsdelta interaction

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (3)

Об асимптотике спектра дифференциального оператора четного порядка с потенциалом дельта-функцией ⋮ On the asymptotic behavior of the spectrum of a sixth-order differential operator, whose potential is the delta function ⋮ Elliptic operators in multidimensional cylinders with frequently alternating boundary conditions along a given curve

Cites Work

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• On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition
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• Bethe-Sommerfeld conjecture
• Bethe-Sommerfeld conjecture for periodic operators with strong perturbations
• Spectral properties of the periodic magnetic Schrödinger operator in the high-energy region. Two-dimensional case
• Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics
• Homogenization of the planar waveguide with frequently alternating boundary conditions
• Asymptotic of the density of states for the Schrödinger operator with periodic electromagnetic potential

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