Hill's potentials in weighted Sobolev spaces and their spectral gaps

DOI10.1007/s00208-010-0513-7zbMath1215.34109arXiv0908.0491OpenAlexW2033166439MaRDI QIDQ621299

Jürgen Pöschel

Publication date: 2 February 2011

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.0491

zbMATH Keywords

Hill's equationgap lengths of the spectrumperiodic and anti-periodic conditionsweighted Gevrey-Sobolev space

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) Inverse problems involving ordinary differential equations (34A55) Linear boundary value problems for ordinary differential equations (34B05)

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Cites Work

• Unnamed Item
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• The asymptotics of the gap in the Mathieu equation
• Spectral gaps of the periodic Schrödinger operator when its potential is an entire function.
• Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps.
• Spectral triangles of Schrödinger operators with complex potentials
• Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
• Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill
• A CHARACTERIZATION OF THE SPECTRUM OF HILL'S OPERATOR
• The inverse problem for periodic potentials
• Gap estimates of the spectrum of Hill’s equation and action variables for KdV
• Instability zones of periodic 1-dimensional Schrödinger and Dirac operators
• Spectral gaps of potentials in weighted Sobolev spaces
• Estimates on the Stability Intervals for Hill's Equation
• Characterization of Hill operators with analytic potentials

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