First order selfadjoint differential operators with involution

İpek Al P., İsmailov Z.

LOBACHEVSKII JOURNAL OF MATHEMATICS, vol.42, pp.496-501, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42
  • Publication Date: 2021
  • Doi Number: 10.1134/s1995080221030045
  • Journal Name: LOBACHEVSKII JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.496-501
  • Keywords: differential operator with involution, selfadjoint differential operator, deficiency indices, space of boundary value, spectrum
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, certain spectral properties related with the first order linear differential-operator expression with involution in the Hilbert space of vector-functions at finite interval have been examined. Firstly, the minimal and maximal operators which are generated by the first order linear differential-operator expression with involution in the Hilbert spaces of vector-functions has been described. Then, the deficiency indices of the minimal operator have been calculated. Moreover, the space of boundary values of the minimal operator have been constructed. Afterwards, by using the method of Calkin-Gorbachuk, the general form of all selfadjoint extensions of the minimal operator in terms of boundary values has been found. Later on, the structure of spectrum of these extensions has been investigated.