TY - JOUR
T1 - Convolution operators on expanding polyhedra
T2 - Limits of the norms of inverse operators and pseudospectra
AU - Maximenko, E. A.
PY - 2003/11/1
Y1 - 2003/11/1
N2 - 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.
AB - 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.
KW - Convolution operator
KW - Norm of inverse operator
KW - Polyhedron
KW - Pseudospectrum
UR - http://www.scopus.com/inward/record.url?scp=3843134961&partnerID=8YFLogxK
U2 - 10.1023/B:SIMJ.0000007478.13348.97
DO - 10.1023/B:SIMJ.0000007478.13348.97
M3 - Artículo
SN - 0037-4466
VL - 44
SP - 1027
EP - 1038
JO - Siberian Mathematical Journal
JF - Siberian Mathematical Journal
IS - 6
ER -