On the Spectral Asymptotics of Operators on Manifolds with Ends

Details On the Spectral Asymptotics of Operators on Manifolds with Ends On the Spectral Asymptotics of Operators on Manifolds with Ends

2012-02-13

arxiv.org/abs/1202.2846v2

Mathematics

Functional Analysis

30 pages

Scientific paper

We deal with the asymptotic behaviour of the counting function of certain positive selfadjoint operators with double order $(m,\mu)$, $m,\mu>0$, $m\not=\mu$, defined on a manifold with ends. The structure of this class of noncompact manifolds allows to make use of calculi of pseudodifferential operators and Fourier Integral Operators associated with weighted symbols, globally defined on R^n. By means of these tools, we improve known results concerning the remainder terms of the corresponding Weyl Formulae, and show how their behaviour depends on the ratio of the two components of the order and on the dimension of the underlying manifold.

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