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Model representations for systems of selfadjoint operators satisfying commutation relations
Sbornik. Mathematics, Tome 201 (2010) no. 10, pp. 1461-1493 Cet article a éte moissonné depuis la source Math-Net.Ru

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Model representations are constructed for a system $\{B_k\}_1^n$ of bounded linear selfadjoint operators in a Hilbert space $H$ such that \begin{gather*} [B_k,B_s]=\frac i2\varphi^*R_{k,s}^-\varphi, \qquad \sigma_k\varphi B_s-\sigma_s\varphi B_k=R_{k,s}^+\varphi, \\ \sigma_k\varphi\varphi^*\sigma_s-\sigma_s\varphi\varphi^*\sigma_k=2iR_{k,s}^-, \qquad 1\le k, s\le n, \end{gather*} where $\varphi$ is a linear operator from $H$ into a Hilbert space $E$ and $\{\sigma_k,R_{k,s}^\pm\}_1^n$ are some selfadjoint operators in $E$. A realization of these models in function spaces on a Riemann surface is found and a full set of invariants for $\{B_k\}_1^n$ is described. Bibliography: 11 titles.
Keywords: systems of selfadjoint operators, model representations.
Mots-clés : commutation relations 
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V. A. Zolotarev. Model representations for systems of selfadjoint operators satisfying commutation relations. Sbornik. Mathematics, Tome 201 (2010) no. 10, pp. 1461-1493. http://geodesic.mathdoc.fr/item/SM_2010_201_10_a2/

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