Displaying similar documents to “Spectral analysis for differential operators with singularities.”

An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point

Alexey Fedoseev (2013)

Open Mathematics

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We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.

Discrete spectrum and principal functions of non-selfadjoint differential operator

Gülen Başcanbaz Tunca, Elgiz Bairamov (1999)

Czechoslovak Mathematical Journal

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In this article, we consider the operator L defined by the differential expression ℓ ( y ) = - y ' ' + q ( x ) y , - ∞ < x < ∞ in L 2 ( - ∞ , ∞ ) , 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 - ∞ < x < ∞ exp ϵ | x | | q ( x ) | < ∞ , ϵ > 0 holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.

Power bounded and exponentially bounded matrices

Jaromír J. Koliha, Ivan Straškraba (1999)

Applications of Mathematics

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The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.