Spectral gap asymptotics of one-dimensional Schrödinger operators with singular periodic potentials
Djakov, Plamen Borissov and Mityagin, Boris (2009) Spectral gap asymptotics of one-dimensional Schrödinger operators with singular periodic potentials. In: International Conference on Linear and Non-Linear Theory of Generalized Functions and its Applications, Bedlewo, Poland
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Official URL: http://dx.doi.org/10.1080/10652460802564837
By using quasi-derivatives we develop a Fourier method for studying the spectral properties of one-dimensional Schrodinger operators with periodic singular potentials. Our results reveal the close relationship between the smoothness of the potential and spectral gap asymptotics under the a priori assumption [image omitted] This extends and strengthens similar results proved in the classical case [image omitted].
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