On Two-Dimensional Model Representations of One Class of Commuting Operators

  • R. Hatamleh
  • V. A. Zolotarev

Abstract

In the work by V. A. Zolotarev, Dokl. Akad. Nauk Arm. SSR, 63, No. 3, 136–140 (1976), a triangular model is constructed for a system of twice-commuting linear bounded completely nonself-adjoint operators {A 1, A 2} ([A 1, A 2] = 0, [A 1 , A 2] = 0) such that rank (A 1) I (A 2) I  = 1 (2i(A k ) I  = A k  − A k k = 1, 2) and the spectrum of each operator A k k = 1, 2, is concentrated at zero. The indicated triangular model has the form of a system of operators of integration over the independent variable in L Ω 2 where the domain Ω = [0, a] × [0, b] is a compact set in ℝ2 bounded by the lines x = a and y = b and a decreasing smooth curve L connecting the points (0, b) and (a, 0).
Published
25.01.2014
How to Cite
HatamlehR., and ZolotarevV. A. “On Two-Dimensional Model Representations of One Class of Commuting Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 1, Jan. 2014, pp. 108–127, http://umj.imath.kiev.ua/index.php/umj/article/view/2115.
Section
Research articles