ON SELFADJOINT DILATION OF THE DISSIPATIVE EXTENSION OF A DIRECT SUM DIFFERENTIAL OPERATOR

Ugurlu E., Allahverdiev B.

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol.7, no.2, pp.194-207, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.15352/bjma/1363784231
  • Title of Journal : BANACH JOURNAL OF MATHEMATICAL ANALYSIS
  • Page Numbers: pp.194-207

Abstract

In this paper, we describe all maximal dissipative, maximal accretive and selfadjoint extensions of the minimal symmetric direct sum differential operators. Further using the equivalence of the Lax-Phillips scattering function and the Sz.-Nagy-Foias, characteristic function we show that all eigen and associated functions of the maximal dissipative extension of the minimal symmetric direct sum operator are complete in L-w(2) (Omega), where Omega = Omega(1) boolean OR Omega(2), Omega(1) = (0, c) and Omega(2) = c, infinity)