Abstract and Applied Analysis
Volume 2013 (2013), Article ID 909782, 21 pages
Research Article

On the Spectral Asymptotics of Operators on Manifolds with Ends

Dipartimento di Matematica, Università degli Studi di Torino, V. C. Alberto, n. 10, I-10123 Torino, Italy

Received 28 September 2012; Accepted 16 December 2012

Academic Editor: Changxing Miao

Copyright © 2013 Sandro Coriasco and Lidia Maniccia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.