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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An example of a periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum
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by R. G. Shterenberg
Translated by: the author
St. Petersburg Math. J. 16 (2005), 417-422
DOI: https://doi.org/10.1090/S1061-0022-05-00858-7
Published electronically: March 9, 2005
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Abstract:

The structure of the lower edge of the spectrum of a periodic magnetic Schrödinger operator is investigated. It is known that in the nonmagnetic case the energy depends quadratically on the quasimomentum in a neighborhood of the lower edge of the spectrum of the operator. An example of a magnetic Schrödinger operator is constructed for which energy is partially degenerate with respect to one component of the quasimomentum.
References
  • Michael Birman and Tatyana Suslina, Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics, Systems, approximation, singular integral operators, and related topics (Bordeaux, 2000) Oper. Theory Adv. Appl., vol. 129, Birkhäuser, Basel, 2001, pp. 71–107. MR 1882692
  • Michael Reed and Barry Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 0493421
  • M. M. Skriganov, Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators, Trudy Mat. Inst. Steklov. 171 (1985), 122 (Russian). MR 798454
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Bibliographic Information
  • R. G. Shterenberg
  • Affiliation: St. Petersburg State University, Department of Physics, Petrodvorets, St. Petersburg 198504, Russia
  • Email: roman@RS3759.spb.edu
  • Received by editor(s): September 1, 2003
  • Published electronically: March 9, 2005
  • Additional Notes: Supported by RFBR (grant no. 02-01-00798).

    • Dedicated: Dedicated to my dear teacher M. Sh. Birman
  • © Copyright 2005 American Mathematical Society
  • Journal: St. Petersburg Math. J. 16 (2005), 417-422
  • MSC (2000): Primary 35J10, 35P15
  • DOI: https://doi.org/10.1090/S1061-0022-05-00858-7
  • MathSciNet review: 2068347