Published January 1, 2009 | Version v1
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Spectral gaps of Schrodinger operators with periodic singular potentials

  • 1. Sabanci Univ, TR-34956 Istanbul, Turkey
  • 2. Ohio State Univ, Dept Math, Columbus, OH 43210 USA

Description

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).

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