Spectral behaviour of a simple non-self-adjoint operator

[摘要] We investigate the spectrum of a typical non-self-adjoint differential operator AD = -d(2) /dx(2) circle timesA acting on L-2 (0, 1) circle times C-2, where A is a 2 x 2 constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate, respectively, at both ends of [0, 1] subset of R. For A is an element of R-2x2 we explore in detail the connection between the entries of A and the spectrum of AD, we find necessary conditions to ensure similarity to a self-adjoint operator and give numerical evidence that suggests a non-trivial spectral evolution. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-11-20

[关键词] spectral theory of non-self-adjoint operators;differential operators;non-real eigenvalues