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