On Two-Dimensional Model Representations of One Class of Commuting Operators
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...
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| Datum: | 2014 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2115 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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). |
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