Spectral gaps of the periodic Schrödinger operator when its potential is an entire function.

DOI10.1016/S0196-8858(03)00027-7zbMath1047.34100OpenAlexW2008336774MaRDI QIDQ1415394

Plamen Djakov, Boris S. Mityagin

Publication date: 3 December 2003

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0196-8858(03)00027-7

zbMATH Keywords

periodic Schrödinger operatorspectral gaps

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)

Related Items (15)

Differentiable functions ⋮ Asymptotics of instability zones of Hill operators with a two term potential ⋮ An anti-periodic LaSalle oscillation theorem for a class of functional differential equations ⋮ Hill's potentials in weighted Sobolev spaces and their spectral gaps ⋮ Anti-periodic solutions for nonlinear evolution equations ⋮ A Schauder and Riesz basis criterion for non-self-adjoint Schrödinger operators with periodic and antiperiodic boundary conditions ⋮ Anti-periodic solutions for fully nonlinear first-order differential equations ⋮ Multiplicities of the eigenvalues of periodic Dirac operators ⋮ An anti-periodic solution for a class of recurrent neural networks ⋮ Anti-periodic solutions for forced Rayleigh-type equations ⋮ Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type ⋮ A criterion for Hill operators to be spectral operators of scalar type ⋮ Simple and double eigenvalues of the Hill operator with a two-term potential ⋮ Instability zones of a periodic 1D Dirac operator and smoothness of its potential ⋮ Riesz basis property of Hill operators with potentials in weighted spaces

Cites Work

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• The asymptotics of the gap in the Mathieu equation
• Gap estimates of the spectrum of the Zakharov-Shabat system
• Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps.
• Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
• Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill
• Gap estimates of the spectrum of Hill’s equation and action variables for KdV
• Estimates on the Stability Intervals for Hill's Equation
• Characterization of Hill operators with analytic potentials

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