Geodesic
Model representations for systems of selfadjoint operators satisfying commutation relations
Sbornik. Mathematics, Tome 201 (2010) no. 10, pp. 1461-1493

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{SM_2010_201_10_a2,
     author = {V. A. Zolotarev},
     title = {Model representations for systems of selfadjoint operators satisfying commutation relations},
     journal = {Sbornik. Mathematics},
     pages = {1461--1493},
     publisher = {mathdoc},
     volume = {201},
     number = {10},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_10_a2/}
}
TY  - JOUR
AU  - V. A. Zolotarev
TI  - Model representations for systems of selfadjoint operators satisfying commutation relations
JO  - Sbornik. Mathematics
PY  - 2010
SP  - 1461
EP  - 1493
VL  - 201
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2010_201_10_a2/
LA  - en
ID  - SM_2010_201_10_a2
ER  - 
%0 Journal Article
%A V. A. Zolotarev
%T Model representations for systems of selfadjoint operators satisfying commutation relations
%J Sbornik. Mathematics
%D 2010
%P 1461-1493
%V 201
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2010_201_10_a2/
%G en
%F SM_2010_201_10_a2
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/