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


Ugurlu E., Allahverdiev B.

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, cilt.7, ss.194-207, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 7 Konu: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.15352/bjma/1363784231
  • Dergi Adı: BANACH JOURNAL OF MATHEMATICAL ANALYSIS
  • Sayfa Sayısı: ss.194-207

Özet

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)