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Homogenization of Periodic Differential Operators as a Spectral Threshold Effect

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New Trends in Mathematical Physics

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Abstract

The present paper is devoted to the homogenization problem for a wide class of periodic second order differential operators (DO’s) in ℝd. This class includes a number of classical DO’s of mathematical physics. We propose a brief survey of the results obtained in a series of Birman and Suslina (Systems, Approximations, Singular Integral Operators and Related Topics, Oper. Theory Adv. Appl., vol. 129, pp. 71–107, 2001; Algebra Anal. 15(5):108, 2003; Algebra Anal. 17(5):69–90, 2005; Algebra Anal. 17(6):1–104, 2005; Algebra Anal. 18(6):1–130, 2006).

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References

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Author information

Authors and Affiliations

  1. Faculty of Physics, St. Petersburg State University, Ulyanovskaya, 3, St. Petersburg, 198504, Russian Federation

    Mikhail S. Birman & Tatiana A. Suslina

Authors
  1. Mikhail S. Birman
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  2. Tatiana A. Suslina
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Correspondence to Tatiana A. Suslina .

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Editors and Affiliations

  1. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro, RJ, Brazil

    Vladas Sidoravičius

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Birman, M.S., Suslina, T.A. (2009). Homogenization of Periodic Differential Operators as a Spectral Threshold Effect. In: Sidoravičius, V. (eds) New Trends in Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2810-5_44

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