Displaying similar documents to “Spectral properties of the Klein–Gordon s -wave equation with spectral parameter-dependent boundary condition.”

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.

A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem

Jamel Ben Amara (2011)

Colloquium Mathematicae

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We study a Sturm-Liouville problem containing a spectral parameter in the boundary conditions. We associate to this problem a self-adjoint operator in a Pontryagin space Π₁. Using this operator-theoretic formulation and analytic methods, we study the asymptotic behavior of the eigenvalues under the variation of a large physical parameter in the boundary conditions. The spectral analysis is applied to investigate the well-posedness and stability of the wave equation of a string. ...

Identification of a wave equation generated by a string

Amin Boumenir (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.

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.