Lagrangian tori and quantization conditions corresponding to spectral series of the Laplace operator on a surface of revolution with conical points

DOI10.1134/S008154381906018XzbMath1440.35223OpenAlexW3012860599MaRDI QIDQ2185516

Andrej I. Shafarevich

Publication date: 4 June 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/s008154381906018x

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Canonical quantization (81S08)

Related Items (1)

Solution of the Cauchy problem for the wave equation on a cone with a non-Friedrichs Laplacian

Cites Work

• Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere
• Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation
• Degenerate wave equation with localized initial data: asymptotic solutions corresponding to various self-adjoint extensions
• Noncompact Lagrangian manifolds corresponding to the spectral series of the Schrödinger operator with delta-potential on a surface of revolution
• Phase space geometry for a wave equation degenerating on the boundary of the domain
• Asymptotics, related to billiards with semi-rigid walls, of eigenfunctions of the \(\nabla D(x)\nabla\) operator in dimension 2 and trapped coastal waves
• The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary
• Spectral series of the Schrödinger operator with delta-potential on a three-dimensional spherically symmetric manifold
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