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


Allahverdiev B. , Bairamov E., Ugurlu E.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.401, no.1, pp.388-396, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 401 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1016/j.jmaa.2012.12.020
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.388-396
  • Keywords: Dissipative operators, Transmission condition, Eigenvalue problem, DIRECT SUM SPACES, EIGENVALUE PARAMETER, SPECTRAL PARAMETER, OPERATORS, THEOREM

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-Foia characteristic function, we show that all eigenfunctions and associated functions are complete in the space L-w(2)(Omega). (C) 2012 Elsevier Inc. All rights reserved.