Asymptotic bounds for spectral bands of periodic Schrödinger operators
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M. M. Skriganov and A. V. Sobolev
Translated by: the authors - St. Petersburg Math. J. 17 (2006), 207-216
- DOI: https://doi.org/10.1090/S1061-0022-06-00900-9
- Published electronically: January 19, 2006
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Abstract:
The precise upper and lower bounds for the multiplicity of the spectrum band overlapping are given for the multidimensional periodic Schrödinger operators with rational period lattices. These bounds are based on very recent results on the lattice point problem.References
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Bibliographic Information
- M. M. Skriganov
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Email: skrig@pdmi.ras.ru
- A. V. Sobolev
- Affiliation: School of Mathematics, University of Birmingham, Edgbaston Birmingham, B152TT, United Kingdom
- Email: asobolev@bham.ac.uk
- Received by editor(s): April 8, 2005
- Published electronically: January 19, 2006
- Additional Notes: The first author was supported by RFBR (grant no. 02-01-00086) and by INTAS (grant no. 00-429).
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 207-216
- MSC (2000): Primary 35P15, 11H06
- DOI: https://doi.org/10.1090/S1061-0022-06-00900-9
- MathSciNet review: 2140682
Dedicated: Dedicated to L. D. Faddeev on his 70th birthday