2017
Том 69
№ 6

All Issues

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

Hatamleh R., Zolotarev V. A.

Full text (.pdf)


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).

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 1, pp 122-144.

Citation Example: Hatamleh R., Zolotarev V. A. On Two-Dimensional Model Representations of One Class of Commuting Operators // Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 108–127.

Full text