Normal Extensions of Differential Operators for Degenerate First-order

SERTBAŞ M., YILMAZ F.

Lobachevskii Journal of Mathematics, vol.45, no.3, pp.1254-1260, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1134/s1995080224600882
  • Journal Name: Lobachevskii Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.1254-1260
  • Keywords: degenerate differential operator, extension, formally normal operator, minimal and maximal operators, normal operator, spectrum
  • Karadeniz Technical University Affiliated: Yes

Abstract

Abstract: In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators.