Eigenparameter dependent Sturm–Liouville problems in boundary conditions with transmission conditions

descriptionPublicationkeyboard_double_arrow_right Article 01 May 2013 Azerbaijan English Publisher:Elsevier BVJournal:Journal of Mathematical Analysis and Applications, volume 401, pages 388-396 (issn: 0022-247X,

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Authors: Allahverdiev, Bilender P.; Bairamov, Elgiz; Ugurlub, Ekin;

doi: 10.1016/j.jmaa.2012.12.020

handle: 20.500.12323/6987

Eigenparameter dependent Sturm–Liouville problems in boundary conditions with transmission conditions

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Abstract

Abstract In this paper, we investigate the nonselfadjoint (dissipative) boundary value transmission problems in Weyl’s limit-circle case. At first using the method of operator-theoretic formulation we pass to a new operator. After showing that this new operator is a maximal dissipative operator, we construct a selfadjoint dilation of the maximal dissipative operator. Using the equivalence of the Lax–Phillips scattering function and the Sz.-Nagy-Foias characteristic function, we show that all eigenfunctions and associated functions are complete in the space L w 2 ( Ω ) .

Country

Azerbaijan

Related Organizations

Khazar University
Azerbaijan
Ankara University
Turkey
Khazar University, Library and Information Center
Azerbaijan
Süleyman Şah University
Turkey

Keywords

Dissipative operators, Eigenvalue problem, Transmission condition

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