Abstract
For one-dimensional non-selfadjoint Schrödinger and Dirac operators with periodic complex-valued potentials belonging to the class \(L_2 \), asymptotic representations for spectral gaps are obtained in terms of Fourier coefficients of the potentials and estimates for the gap lengths are given.
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ACKNOWLEDGMENTS
The author is grateful to A.M. Savchuk and I.V. Sadovnichaya for valuable advice, which has made for an improvement of the paper.
Funding
This work was supported by a grant from the President of the Russian Federation for young candidates of sciences, project no. MK-1056.2018.1, agreement no. 075-02-2018-433.
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Translated by V. Potapchouck
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Polyakov, D.M. Estimates of Spectral Gap Lengths for Schrödinger and Dirac Operators. Diff Equat 56, 585–594 (2020). https://doi.org/10.1134/S0012266120050043
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DOI: https://doi.org/10.1134/S0012266120050043