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Discrete spectrum of a two-dimensional periodic elliptic second order operator perturbed by a decaying potential. II. Internal gaps


Author: T. A. Suslina
Translated by: the author
Original publication: Algebra i Analiz, tom 15 (2003), nomer 2.
Journal: St. Petersburg Math. J. 15 (2004), 249-287
MSC (2000): Primary 35P20
DOI: https://doi.org/10.1090/S1061-0022-04-00810-6
Published electronically: January 29, 2004
MathSciNet review: 2052132
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Abstract: The discrete spectrum in the spectral gaps is studied in the case of a two-dimensional periodic elliptic second order operator perturbed by a decaying potential. The main goal is to find asymptotics (for the large coupling constant) of the number of eigenvalues that have been ``born'' (or have ``died'') at the edges of the gap. The high-energy (Weyl) asymptotics and the threshold asymptotics are distinguished. At the right edge of the gap, a competition between the Weyl contribution and the threshold contribution may occur. The case of a semiinfinite gap was studied in part I of the paper.


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Additional Information

T. A. Suslina
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 1, Petrodvorets, St. Petersburg 198904, Russia
Email: tanya@petrov.stoic.spb.su

DOI: https://doi.org/10.1090/S1061-0022-04-00810-6
Keywords: Periodic operator, perturbation, discrete spectrum, spectral gap, threshold effect
Received by editor(s): January 14, 2003
Published electronically: January 29, 2004
Additional Notes: Supported by RFBR (grant no. 02-01-00798)
Dedicated: Dedicated to my dear teacher Mikhail Shlemovich Birman on the occasion of his anniversary
Article copyright: © Copyright 2004 American Mathematical Society

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