Spectral analysis of eigenparameter dependent boundary value transmission problems

Ugurlu E., BAYRAM E.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.413, no.1, pp.482-494, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 413 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1016/j.jmaa.2013.11.022
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.482-494
  • Keywords: Dissipative operator, Transmission conditions, Characteristic function, Scattering function, Completeness theorem, STURM-LIOUVILLE PROBLEMS, EIGENVALUE PARAMETER, OPERATORS
  • Ankara University Affiliated: Yes

Abstract

In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with, the boundary value transmission problems on the suitable Hilbert. spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which re established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces. (C) 2013 Elsevier Inc. All rights reserved.