SCATTERING AND SPECTRAL PROBLEMS OF THE DIRECT SUM STURM-LIOUVILLE OPERATORS


Allahverdiev B. P. , Ugurlu E.

APPLIED AND COMPUTATIONAL MATHEMATICS, vol.16, no.3, pp.257-268, 2017 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 3
  • Publication Date: 2017
  • Title of Journal : APPLIED AND COMPUTATIONAL MATHEMATICS
  • Page Numbers: pp.257-268

Abstract

In this paper a space of boundary values is constructed for direct sum minimal symmetric Sturm-Liouville operators and description of all maximal dissipative, maximal accumulative, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions. We construct a selfadjoint dilation of dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.