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- Title
On Two-Dimensional Model Representations of One Class of Commuting Operators.
- Authors
Hatamleh, R.; Zolotarev, V.
- 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, A} ([ A, A] = 0, [ A, A] = 0) such that rank ( A)( A) = 1 (2 i( A) = A − A, k = 1, 2) and the spectrum of each operator A, 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 where the domain Ω = [0, a] × [0, b] is a compact set in ℝ bounded by the lines x = a and y = b and a decreasing smooth curve L connecting the points (0 , b) and ( a, 0) .
- Subjects
TWO-dimensional models; COMMUTING operators (Quantum mechanics); ZOLOTAREV, V. A.; MATHEMATICAL domains; SET theory; NONSELFADJOINT operators
- Publication
Ukrainian Mathematical Journal, 2014, Vol 66, Issue 1, p122
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-014-0916-9