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On the asymptotic distribution of the spectrum of an operator over irreducible representations of its symmetry group. (English. Russian original) Zbl 1142.58308
Funct. Anal. Appl. 40, No. 3, 225-227 (2006); translation from Funkts. Anal. Prilozh. 40, No. 3, 72-75 (2005).
Summary: We prove that a representation of a finite group in the eigenfunction space of an elliptic operator defined on a Riemannian manifold and commuting with the effective action of the group is asymptotically a multiple of the regular representation of the group.
MSC:
58J37 Perturbations of PDEs on manifolds; asymptotics
35P20 Asymptotic distributions of eigenvalues in context of PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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