Spectral Behaviour of a Simple Non-self-adjoint Operator
نویسندگان
چکیده
We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d2/dx2 ⊗ A acting on L(0, 1) ⊗ C, 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 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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تاریخ انتشار 2001