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 $N_P(\lambda )$ of certain positive selfadjoint operators $P$ with double order $(m,\mu )$, $m,\mu >0$, $m\ne \mu$, 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 ${\mathbb{R}}^n$. By means of these tools, we improve known results concerning the remainder terms of the Weyl Formulae for $N_P(\lambda )$ and show how their behaviour depends on the ratio $\frac{m}{\mu }$ and the dimension of $M$.

Final version, 30 pages

References in corpus (1)

• Wodzicki Residue for Operators on Manifolds with Cylindrical Ends

Cited by in corpus (6)

• The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions
• Analysis on singular spaces: Lie manifolds and operator algebras
• Calculus, continuity and global wave-front properties for Fourier integral operators on ${\mathbf{R}}^d$
• Fourier integral operators algebra and fundamental solutions to hyperbolic systems with polynomially bounded coefficients on R^n
• Weyl asymptotics for tensor products of operators and Dirichlet divisors
• Sharp Weyl Estimates for Tensor Products of Pseudodifferential Operators