On the Compactly Solvable Differential Operators for First Order


İPEK AL P. , AKBABA Ü.

Lobachevskii Journal of Mathematics, vol.41, no.6, pp.1078-1086, 2020 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.1134/s1995080220060116
  • Title of Journal : Lobachevskii Journal of Mathematics
  • Page Numbers: pp.1078-1086
  • Keywords: differential operator, solvable extension, spectrum, Schatten-von Neumann classes

Abstract

In this paper, by using the methods of the operator theory, the general form of all compactly solvable extension of the minimal operator which is generated by the first order linear differential operator expression in the Hilbert spaces of vector-functions on finite interval has been found. Later on, the spectrum set of the compactly solvable extensions has been investigated. In addition, the asymptotical behavior of the eigenvalues of any inverse of compactly solvable extension has been studied. Finally, the necessary and sufficient condition for the inverse of the compactly solvable extensions to be belong to Schatten-von Neumann classes has been given.