Spectrum of the One-dimensional Schrödinger Operator With a Periodic Potential Subjected to a Local Dilative Perturbation |
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Authors: | Leonid Zelenko |
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Affiliation: | (1) Department of Mathematics, University of Haifa, Haifa, 31905, Israel |
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Abstract: | We study the spectrum of the one-dimensional Schr?dinger operator with a potential, whose periodicity is violated via a local dilation. We obtain conditions under which this violation preserves the essential spectrum of the Schr?dinger operator and an infinite number of isolated eigenvalues appear in a gap of the essential spectrum. We show that the considered perturbation of the periodic potential is not relative compact in general. |
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Keywords: | Primary 47F05 Secondary 47E05, 35Pxx |
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