Spectral Properties of Non-Self-Adjoint Operators in the Semi-classical Regime

2000/03/07 by P. Redparth, Redparth, P.
Mathematics · #33C10 #34L20 #34L40 #34M40 #47E05 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:33C10 #msc:34L20 #msc:34L40 #msc:34M40 #msc:47E05

paper · pdf · doi:10.48550/arxiv.math/0003044

17 pages, 3 figures

arxiv created 2000/03/07 · arxiv updated 2009/11/30

Abstract

We give a spectral description of the semi-classical Schrodinger operator with a piecewise linear, complex valued potential. Moreover, using these results, we show how an arbitrarily small bounded perturbation of a non-self-adjoint operator can completely change the spectrum of the operator.

Related

• The Pseudospectral Properties of non-self-adjoint Schrödinger Operators in the semi-classical limit
• Non-symmetric perturbations of self-adjoint operators
• Semi-classical Analysis and Pseudospectra
• Semi-Classical Behavior of the Spectral Function
• Construction of self-adjoint differential operators with prescribed spectral properties