The essential spectrum of an operator arising in 2‐dimensional magneto‐hydrodynamics

Abstract

Descloux and Geymonat considered a model problem for a plasma in a toroidal configuration and conjectured that the essential spectrum has an explicitly given band structure. This conjecture was recently proved by Faierman, Mennicken, and Moller by employing an operator matrix representation of the problem. In this paper we discuss the behaviour of the essential spectrum under a perturbation of the original problem. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim