## Abstract and Applied Analysis

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

#### Abstract

We deal with the asymptotic behaviour, for $\lambda \to +\infty$, of the counting function ${N}_{P}\left(\lambda \right)$ of certain positive self-adjoint operators P with double order $\left(m,\mu \right)$, $m,\mu$ > $0, m\ne \mu$ , 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 ${ℝ}^{n}$. By means of these tools, we improve known results concerning the remainder terms of the Weyl Formulae for ${N}_{P}\left(\lambda \right)$ and show how their behaviour depends on the ratio $m/\mu$ and the dimension of M.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 909782, 21 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511841

Digital Object Identifier
doi:10.1155/2013/909782

Mathematical Reviews number (MathSciNet)
MR3044996

Zentralblatt MATH identifier
1274.35255

#### Citation

Coriasco, Sandro; Maniccia, Lidia. On the Spectral Asymptotics of Operators on Manifolds with Ends. Abstr. Appl. Anal. 2013 (2013), Article ID 909782, 21 pages. doi:10.1155/2013/909782. https://projecteuclid.org/euclid.aaa/1393511841

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