Spectral behaviour of a simple non-self-adjoint operator

2001/02/21 by L. S. Boulton, Boulton, L. S.
Mathematics · #34L05 #34L16 #47E05 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:34L05 #msc:34L16 #msc:47E05

paper · pdf · doi:10.48550/arxiv.math/0102170

42 pages, 6 figures

arxiv created 2001/05/15 · arxiv updated 2009/11/30

Abstract

We investigate the spectrum of a typical non-self-adjoint differential operator AD=-d²/dx²⊗ A acting on \Lp(0,1)⊗ ℂ², where A is a 2× 2 constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of [0,1]⊂ℝ. For A∈ ℝ^{2× 2} 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.

Related

• Construction of self-adjoint differential operators with prescribed spectral properties
• Spectral theory of some non-selfadjoint linear differential operators
• Spectral Properties of Non-Self-Adjoint Operators in the Semi-classical Regime
• An analysis of non-selfadjoint first-order differential operators with non-local point interactions
• Spectral properties of non-self-adjoint operators