Singular equivariant asymptotics and Weyl's law

Details Singular equivariant asymptotics and Weyl's law Singular equivariant asymptotics and Weyl's law

2010-01-10

arxiv.org/abs/1001.1515v3

Mathematics

Spectral Theory

53 pages, revised, augmented version

Scientific paper

We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the isotypic components, and relate it with the reduction of the corresponding Hamiltonian flow, proving that the equivariant spectral counting function satisfies Weyl's law, together with an estimate for the remainder.

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