The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution
of eigenvalues, is one of the central problems in the spectral theory of partial differential …

The Problem of the Spectral Asymptotics, in particular the problem of the Asymptotic
Distribution of the Eigenvalues, is one of the central problems in the Spectral Theory of …

Let D be a smooth strictly convex region in R2 containing the origin. Let AD= jAx, xf D|. A
classical theorem of Van der Corput says that the number of lattice points in AD is equal to …

As the subject of extensive research for over a century, spectral asymptotics for partial
differential operators attracted the attention of many outstanding mathematicians and …

The main part of theses notes from the NATO ASI on microlocal analysis and spectral theory
at Ti Ciocco, Sept.-Oct. 1996, is devoted to a new trace formula for resonances, which is …

We classify the points of the spectrum a (A) of a selfadjoint operator A into two main
classes:(i) isolated eigenvalues of finite multiplicity and (ii) all other spectral singularities …

This book originates with a course MZ taught at UC Berkeley during the spring semester of
2003, notes for which LCE took in class. In this presentation we have tried hard to work out …

We consider the localization of eigenfunctions for the operator L=− div A grad+ V on a
Lipschitz domain Ω and, more generally, on manifolds with and without boundary. In earlier …

The purpose of this paper is to establish sharp polynomial bounds on the number of
scattering poles for a general class of compactly supported self-adjoint perturbations of the …

Abstract We consider the Dirichlet Laplacian Δ∈ in a family of bounded domains {− a< x< b,
0< y< ε h (x)}. The main assumption is that x= 0 is the only point of global maximum of the …