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SPECTRAL INSTABILITY OF SEMICLASSICAL OPERATORS
"... Abstract. We give a short review of the spectral instability of non-normal semiclassical differential operators, both for scalar operators and systems. 1. ..."
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Abstract. We give a short review of the spectral instability of non-normal semiclassical differential operators, both for scalar operators and systems. 1.
KCL-MTH-01-07 SPECTRAL BEHAVIOUR OF A SIMPLE NON-SELF-ADJOINT OPERATOR
, 2001
"... Abstract. We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d 2 /dx 2 ⊗ A acting on L 2 (0, 1) ⊗ C 2, 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] ⊂ ..."
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Abstract. We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d 2 /dx 2 ⊗ A acting on L 2 (0, 1) ⊗ C 2, 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. 1.
Dedicated to V.G. Maz’ya
, 906
"... Resolvent estimates for non-self-adjoint operators via semi-groups ..."
