Dissipative Sturm-Liouville operators in limit-point case

Allahverdiev B.

ACTA APPLICANDAE MATHEMATICAE, vol.86, no.3, pp.237-248, 2005 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 86 Issue: 3
  • Publication Date: 2005
  • Doi Number: 10.1007/s10440-004-7026-x
  • Journal Name: ACTA APPLICANDAE MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.237-248

Abstract

Dissipative singular Sturm-Liouville operators are studied in the Hilbert space L-w(2) [a, b) (-infinity < a < b <= infinity), that the extensions of a minimal symmetric operator in Weyl's limit-point case. We construct a selfadjoint dilation of the 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 in terms of the Titchmarsh-Weyl function of a selfadjoint operator. Finally, ill the case when the Titchmarsh-Weyl function of the selfadjoint operator is a meromorphic in complex plane, we prove theorems oil completeness of the system of eigenfunctions and associated functions of the dissipative Sturm-Liouville operators.