Asymptotics of instability zones of the Hill operator with a two term potential

DOI10.1016/j.jfa.2006.06.013zbMath1115.34079arXivmath-ph/0509034OpenAlexW1980207129MaRDI QIDQ859642

Plamen Djakov, Boris S. Mityagin

Publication date: 16 January 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0509034

zbMATH Keywords

asymptotics of spectral gapstwo-term potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items

Oscillation problems for Hill's equation with periodic damping ⋮ Nonoscillation of the Mathieu-type half-linear differential equation and its application to the generalized Whittaker-Hill-type equation ⋮ Combinatorial identities related to eigen-function decompositions of Hill operators: open questions ⋮ Divergence of spectral decompositions of Hill operators with two exponential term potentials ⋮ Refined asymptotics of the spectral gap for the Mathieu operator ⋮ Spectral triangles of non-selfadjoint Hill and Dirac operators ⋮ Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials ⋮ Riesz bases consisting of root functions of 1D Dirac operators ⋮ One-dimensional quasi-exactly solvable Schrödinger equations ⋮ Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators ⋮ Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials ⋮ Whittaker–Hill equation and semifinite-gap Schrödinger operators ⋮ Riesz basis property of Hill operators with potentials in weighted spaces ⋮ Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem

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