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Convolution operators on expanding polyhedra: limits of the norms of inverse operators and pseudospectra. (Russian, English) Zbl 1071.47013
Sib. Mat. Zh. 44, No. 6, 1310-1323 (2003); translation in Sib. Math. J. 44, No. 6, 1027-1038 (2003).
The author considers matrix convolution operators with integrable kernels on expanding polyhedra. He studies their connection with convolution operators on the cones at the vertices of polyhedra and proves 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 is based on the local method adapted to this kind of problems.
MSC:
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
44A35 Convolution as an integral transform
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