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manuscripta mathematica

, Volume 95, Issue 3, pp 363–376 | Cite as

Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights

  • A. Böttcher
  • Y.I. Karlovich
  • V.S. Rabinovich

Abstract:

We show that by using Mellin pseudodifferential operators whose double symbol depends analytically on the co-variable we can rather quickly arrive at descriptions of the local spectra of the Cauchy singular integral operator over a large class of Carleson curves with Muckenhoupt weights. The approach of this paper extends some recent results of the spectral theory of singular integral operators to the case of piecewise slowly varying coefficients and also yields new and surprising interpretations of these results.

Mathematics Subject Classification (1991):Primary: 47 B 35;¶Secondary: 42 A 50, 45 E 05, 46 N 20, 47 G 30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • A. Böttcher
    • 1
  • Y.I. Karlovich
    • 2
  • V.S. Rabinovich
    • 3
  1. 1.Technische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Germany.¶e-mail: aboettch@mathematik.tu-chemnitz.deDE
  2. 2.Ukrainian Academy of Sciences, Marine Hydrophysical Institute,¶Hydroacoustic Department, Preobrazhenskaya Street 3, 270 100 Odessa, Ukraine.¶e-mail: karlik@imem.odessa.ua}UA
  3. 3.Rostov-on-Don State University, Faculty of Mechanics and Mathematics, Bolshaya Sa‐dovaya Street 105, 344 711 Rostov-on-Don, Russia.¶e-mail: rabinov@ns.unird.ac.ru}RU

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