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

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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.
Original languageAmerican English
Pages (from-to)1027-1038
Number of pages923
JournalSiberian Mathematical Journal
DOIs
StatePublished - 1 Nov 2003

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Pseudospectra
Convolution Operator
Convolution
Polyhedron
Mathematical operators
Norm
Cones
Cone
Operator
Tend
matrix
Union
kernel
norm
method

Cite this

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title = "Convolution operators on expanding polyhedra: Limits of the norms of inverse operators and pseudospectra",
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.",
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