Displaying similar documents to “Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems.”

On the characterization of scalar type spectral operators

P. A. Cojuhari, A. M. Gomilko (2008)

Studia Mathematica

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The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.

On discreteness of spectrum of a functional differential operator

Sergey Labovskiy, Mário Frengue Getimane (2014)

Mathematica Bohemica

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We study conditions of discreteness of spectrum of the functional-differential operator ℒ u = - u ' ' + p ( x ) u ( x ) + ∫ - ∞ ∞ ( u ( x ) - u ( s ) ) d s r ( x , s ) on ( - ∞ , ∞ ) . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.

On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator

S. M. Bahri (2012)

Mathematica Bohemica

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In the present work, using a formula describing all scalar spectral functions of a Carleman operator A of defect indices ( 1 , 1 ) in the Hilbert space L 2 ( X , μ ) that we obtained in a previous paper, we derive certain results concerning the localization of the spectrum of quasi-selfadjoint extensions of the operator A .