Spectral behaviour of a simple non-self-adjoint operator

Lyonell S. Boulton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We investigate the spectrum of a typical non-self-adjoint differential operator AD = -d2/dx2 ⊗ A acting on L2(0, 1) ⊗ C2, 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] ⊂ ℝ. For A ε ℝ2×2 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.

Original languageEnglish
Pages (from-to)186-229
Number of pages44
JournalJournal of Differential Equations
Issue number1
Publication statusPublished - 20 Nov 2002


  • Differential operators
  • Non-real eigenvalues
  • Spectral theory of non-self-adjoint operators

ASJC Scopus subject areas

  • Analysis


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