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Spectral gaps of Schrödinger operators with periodic singular potentials

By Plamen Borissov Djakov and Boris Samuel Mityagin


By using quasi-derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schrodinger operators with periodic singular potentials v. Our results reveal a close relationship between smoothness of potentials and spectral gap asymptotics under a priori assumption v is an element of H-loc(-1)(R). They extend and strengthen similar results proved in the classical case v is an element of L-loc(2)(R)

Topics: QA299.6-433 Analysis
Publisher: International Press
Year: 2009
DOI identifier: 10.4310/dpde.2009.v6.n2.a1
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