NORMAL DIFFERENTIAL OPERATORS OF THIRD-ORDER

İSMAİLOV Z., Erol M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.41, no.5, pp.675-688, 2012 (SCI-Expanded, Scopus, TRDizin) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 5
  • Publication Date: 2012
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.675-688
  • Karadeniz Technical University Affiliated: Yes

Abstract

In the Hilbert space of vector-functions L-2(H, (a, b)), where H is any separable Hilbert space, the general representation in terms of boundary values of all normal extensions of the formally normal minimal operator, generated by linear differential-operator expressions of third order in the form l(u) = (u)''' (t) + A(3)u(t), A : D(A) subset of H -> H, A = A* >= E, is obtained in the first part of this study. Then, some spectral properties of these normal extensions are investigated. In particular, the case of A(-1) is an element of G(infinity)(H), asymptotic estimates of normal extensions of eigenvalues has been established at infinity.