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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.

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On homogenization procedure for periodic operators near the edge of an internal gap
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by M. Sh. Birman
Translated by: T. A. Suslina
St. Petersburg Math. J. 15 (2004), 507-513
DOI: https://doi.org/10.1090/S1061-0022-04-00819-2
Published electronically: July 6, 2004
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References
  • Alain Bensoussan, Jacques-Louis Lions, and George Papanicolaou, Asymptotic analysis for periodic structures, Studies in Mathematics and its Applications, vol. 5, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 503330
  • N. S. Bakhvalov and G. P. Panasenko, Osrednenie protsessov v periodicheskikh sredakh, “Nauka”, Moscow, 1984 (Russian). Matematicheskie zadachi mekhaniki kompozitsionnykh materialov. [Mathematical problems of the mechanics of composite materials]. MR 797571
  • V. V. Zhikov, S. M. Kozlov, and O. A. Oleĭnik, Usrednenie differentsial′nykh operatorov, “Nauka”, Moscow, 1993 (Russian, with English and Russian summaries). MR 1318242
  • V. V. Zhikov, Spectral approach to asymptotic diffusion problems, Differentsial′nye Uravneniya 25 (1989), no. 1, 44–50, 180 (Russian); English transl., Differential Equations 25 (1989), no. 1, 33–39. MR 986395
  • Carlos Conca and Muthusamy Vanninathan, Homogenization of periodic structures via Bloch decomposition, SIAM J. Appl. Math. 57 (1997), no. 6, 1639–1659. MR 1484944, DOI 10.1137/S0036139995294743
  • 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
  • M. Sh. Birman, The discrete spectrum in gaps of the perturbed periodic Schrödinger operator. II. Nonregular perturbations, Algebra i Analiz 9 (1997), no. 6, 62–89 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 9 (1998), no. 6, 1073–1095. MR 1610239
  • M. Š. Birman and M. Z. Solomjak, Estimates for the singular numbers of integral operators, Uspehi Mat. Nauk 32 (1977), no. 1(193), 17–84, 271 (Russian). MR 0438186
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Bibliographic Information
  • M. Sh. Birman
  • Affiliation: Department of Physics, St. Petersburg State University, Ul’ynovskaya 1, Petrodvorets, St. Petersburg, 198504, Russia
  • Email: tanya@petrov.stoic.spb.su
  • Received by editor(s): June 2, 2003
  • Published electronically: July 6, 2004
  • Additional Notes: Supported by RFBR (grant no. 02-01-00798).
  • © Copyright 2004 American Mathematical Society
  • Journal: St. Petersburg Math. J. 15 (2004), 507-513
  • MSC (2000): Primary 35P99
  • DOI: https://doi.org/10.1090/S1061-0022-04-00819-2
  • MathSciNet review: 2068979