Spectral gaps of Schrödinger operators with periodic singular potentials
Djakov, Plamen Borissov and Mityagin, Boris Samuel (2009) Spectral gaps of Schrödinger operators with periodic singular potentials. Dynamics of Partial Differential Equations, 6 (2). pp. 95-165. ISSN 1548-159X
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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