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On the Spectral Asymptotics of Operators on Manifolds with Ends

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  • Sandro Coriasco
  • Lidia Maniccia

Abstract

We deal with the asymptotic behaviour, for , of the counting function of certain positive self-adjoint operators P with double order , > , defined on a manifold with ends M . 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 . By means of these tools, we improve known results concerning the remainder terms of the Weyl Formulae for and show how their behaviour depends on the ratio and the dimension of M .

Suggested Citation

  • Sandro Coriasco & Lidia Maniccia, 2013. "On the Spectral Asymptotics of Operators on Manifolds with Ends," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-21, April.
    • Handle: RePEc:hin:jnlaaa:909782
    DOI: 10.1155/2013/909782
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