Spectral behaviour of a simple non-self-adjoint operator

Lyonell S. Boulton

doi:10.1016/S0022-0396(02)00003-7

Spectral behaviour of a simple non-self-adjoint operator

Lyonell S. Boulton^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 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.

Original language	English
Pages (from-to)	186-229
Number of pages	44
Journal	Journal of Differential Equations
Volume	186
Issue number	1
DOIs	https://doi.org/10.1016/S0022-0396(02)00003-7
Publication status	Published - 20 Nov 2002

Keywords

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

ASJC Scopus subject areas

Analysis

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10.1016/S0022-0396(02)00003-7

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abstract = "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.",

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N2 - 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.

AB - 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.

KW - Differential operators

KW - Non-real eigenvalues

KW - Spectral theory of non-self-adjoint operators

UR - https://www.scopus.com/pages/publications/0037146370

U2 - 10.1016/S0022-0396(02)00003-7

DO - 10.1016/S0022-0396(02)00003-7

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VL - 186

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EP - 229

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Spectral behaviour of a simple non-self-adjoint operator

Abstract

Keywords

ASJC Scopus subject areas

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