Krein's Theorem for the Dissipative Operators with Finite Impulsive Effects

Ugurlu E., BAYRAM E.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.36, no.2, pp.256-270, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1080/01630563.2014.970642
  • Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.256-270
  • Keywords: 34B20, 34B24, 34B37, Dissipative operators, Krein's theorem, Impulsive condition, Completeness, STURM-LIOUVILLE PROBLEMS, BOUNDARY-VALUE PROBLEM, LIMIT-CIRCLE CRITERIA, TRANSMISSION CONDITIONS
  • Ankara University Affiliated: Yes

Abstract

In this article, singular dissipative operators with finite impulsive conditions are investigated. In particular, after passing to the inverse operators, it is obtained that the imaginary parts of the inverse operators are nuclear. Finally, using Krein's theorem, it is proved that all root vectors of the singular dissipative operators with finite impulsive conditions are complete in the Hilbert space.