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Estimates and Spectral Asymptotics for Systems with Multiplicities

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Abstract

We consider elliptic and hyperbolic systems with diagonalizable principal part. Characteristics are allowed to have variable multiplicities. Assuming that the characteristics are generic, we give estimates for solutions of a hyperbolic Cauchy problem in L p spaces. The first and second terms of the spectral asymptotics are obtained for the corresponding elliptic system.

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Authors and Affiliations

  1. St. Petersburg Branch of V. A. Steklov Mathematical Institute (POMI), St. Petersburg, Russia

    I. V. Kamotski

  2. Imperial College, London

    M. V. Ruzhansky

Authors
  1. I. V. Kamotski
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  2. M. V. Ruzhansky
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__________

Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 4, pp. 78–80, 2005

Original Russian Text Copyright © by I. V. Kamotski and M. V. Ruzhansky

Research was supported by EPSRC grant No. GR/R67583/01.

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Kamotski, I.V., Ruzhansky, M.V. Estimates and Spectral Asymptotics for Systems with Multiplicities. Funct Anal Its Appl 39, 308–310 (2005). https://doi.org/10.1007/s10688-005-0052-2

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  • DOI: https://doi.org/10.1007/s10688-005-0052-2

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