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Discrete spectrum and principal functions of non-selfadjoint differential operator

Gülen Başcanbaz Tunca; Elgiz Bairamov — 1999

Czechoslovak Mathematical Journal

In this article, we consider the operator $L$ defined by the differential expression $ℓ (y) = - y^{''} + q (x) y, - \infty < x < \infty$ in $L_{2} (- \infty, \infty)$ , where $q$ is a complex valued function. Discussing the spectrum, we prove that $L$ has a finite number of eigenvalues and spectral singularities, if the condition $sup_{- \infty < x < \infty} \{exp (ϵ \sqrt{| x |}) | q (x) |\} < \infty, ϵ > 0$ holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.

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Discrete spectrum and principal functions of non-selfadjoint differential operator

Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions.

Non-self-adjoint singular Sturm-Liouville problems with boundary conditions dependent on the eigenparameter.

Jost solution and the spectrum of the discrete Dirac systems.