A self adjoint expansion of a symmetric differential operator with operator coefficient


Karayel S. , Adıgüzelov E.

Int. J. Contemp. Math. Sci., Vol. 2, No. 22, s. 1053-1067., vol.2, no.66, pp.1053-1067, 2007 (Refereed Journals of Other Institutions)

  • Publication Type: Article / Article
  • Volume: 2 Issue: 66
  • Publication Date: 2007
  • Doi Number: 10.12988/ijcms.2007.07107
  • Title of Journal : Int. J. Contemp. Math. Sci., Vol. 2, No. 22, s. 1053-1067.
  • Page Numbers: pp.1053-1067

Abstract

In this work, we prove that the closure of a symmetric operator L0 which is formed by differential expression (L0y)(x) = −(p(x)y (x)) − Q(x)y(x) and with the boundary condition cos α.y(0) + sinα.y (0) = 0 is self adjoint where α ∈ (−∞,∞) in the space L2(0,∞; H ). Furthermore, we investigate some properties of this operator. Mathematics Subject Classification: 47A10, 34L20 Keywords: Closure, Hilbert Space, Self-Adjoint Operator, Symmetric Operator