Location and Weyl Formula for the Eigenvalues of Some Non Self-Adjoint Operators

Abstract

We present a survey of some recent results concerning the location and the Weyl formula for the complex eigenvalues of two non self-adjoint operators. We study the eigenvalues of the generator G of the contraction semigroup e tG , t ≥ 0, related to the wave equation in an unbounded domain Ω with dissipative boundary conditions on ∂ Ω . Also one examines the interior transmission eigenvalues (ITE) in a bounded domain K obtaining a Weyl formula with remainder for the counting function N(r) of complex (ITE). The analysis is based on a semi-classical approach.