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Siberian Mathematical Journal

, Volume 44, Issue 6, pp 1027–1038 | Cite as

Convolution Operators on Expanding Polyhedra: Limits of the Norms of Inverse Operators and Pseudospectra

  • E. A. Maximenko
Article
  • 27 Downloads

Abstract

We consider matrix convolution operators with integrable kernels on expanding polyhedra. We study their connection with convolution operators on the cones at the vertices of polyhedra. We prove that the norm of the inverse operator on a polyhedron tends to the maximum of the norms of the inverse operators on the cones, and the pseudospectrum tends to the union of the corresponding pseudospectra. The study bases on the local method adapted to this kind of problems.

convolution operators polyhedra norm of inverse operator pseudospectrum 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • E. A. Maximenko
    • 1
  1. 1.Rostov State UniversityRostov-on-Don

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