726 research outputs found
Resolvents of cone pseudodifferential operators, asymptotic expansions and applications
We study the structure and asymptotic behavior of the resolvent of elliptic
cone pseudodifferential operators acting on weighted Sobolev spaces over a
compact manifold with boundary. We obtain an asymptotic expansion of the
resolvent as the spectral parameter tends to infinity, and use it to derive
corresponding heat trace and zeta function expansions as well as an analytic
index formula.Comment: 30 pages, 5 figure
On the Noncommutative Residue and the Heat Trace Expansion on Conic Manifolds
Given a cone pseudodifferential operator we give a full asymptotic
expansion as of the trace \Tr Pe^{-tA}, where is an elliptic
cone differential operator for which the resolvent exists on a suitable region
of the complex plane. Our expansion contains and new
terms whose coefficients are given explicitly by means of residue traces. Cone
operators are contained in some natural algebras of pseudodifferential
operators on which unique trace functionals can be defined. As a consequence of
our explicit heat trace expansion, we recover all these trace functionals.Comment: 15 page
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