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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1310–1323 (Mi smj1257)  

Convolution operators on expanding polyhedra: limits of the norms of inverse operators and pseudospectra

E. A. Maksimenko

Rostov State University

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.

Keywords: convolution operator, polyhedron, norm of inverse operator, pseudospectrum

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English version:
Siberian Mathematical Journal, 2003, 44:6, 1027–1038

Bibliographic databases:

UDC: 517.983.34
Received: 14.05.2003

Citation: E. A. Maksimenko, “Convolution operators on expanding polyhedra: limits of the norms of inverse operators and pseudospectra”, Sibirsk. Mat. Zh., 44:6 (2003), 1310–1323; Siberian Math. J., 44:6 (2003), 1027–1038

Citation in format AMSBIB
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\by E.~A.~Maksimenko
\paper Convolution operators on expanding polyhedra: limits of the norms of inverse operators and pseudospectra
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1310--1323
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034937}
\zmath{https://zbmath.org/?q=an:1071.47013}
\elib{http://elibrary.ru/item.asp?id=13872436}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 1027--1038
\crossref{https://doi.org/10.1023/B:SIMJ.0000007478.13348.97}
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