Spectral gap asymptotics of one-dimensional Schrödinger operators with singular periodic potentials

DOI10.1080/10652460802564837zbMath1176.34108OpenAlexW2060107326MaRDI QIDQ3619812

Boris S. Mityagin, Plamen Djakov

Publication date: 9 April 2009

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460802564837

zbMATH Keywords

Schrödinger operatorspectral gapssingular periodic potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items

Strict domain monotonicity of the principal eigenvalue and a characterization of lower boundedness for the Friedrichs extension of four-coefficient Sturm–Liouville operators, Reconstruction of the potential of the Sturm-Liouville operator from a finite set of eigenvalues and normalizing constants, Solving the inverse Sturm-Liouville problem with singular potential and with polynomials in the boundary conditions, Bari–Markus property for Riesz projections of 1D periodic Dirac operators, Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville operator with singular potential, Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators, Equiconvergence of spectral decompositions of Hill operators, The damped string problem revisited, Direct and inverse problems for the matrix Sturm-Liouville operator with general self-adjoint boundary conditions, Convergence of expansions in Schrödinger and Dirac eigenfunctions, with an application to the R-matrix theory, Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem, Solving An Inverse Problem For The Sturm-Liouville Operator With A Singular Potential By Yurko's Method

Cites Work

• Sturm-Liouville differential operators in direct sum spaces
• Spectral theory of ordinary differential operators
• Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps.
• Transformation operators for Sturm--Liouville operators with singular potentials
• Spectral triangles of Schrödinger operators with complex potentials
• Eigenvalue asymptotics for Sturm--Liouville operators with singular potentials
• Discrete and continuous boundary problems
• Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
• Gap estimates of the spectrum of Hill’s equation and action variables for KdV
• Inverse spectral problems for Sturm Liouville operators with singular potentials
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item