# Journal of Operator Theory

Volume 44, Issue 2, Fall 2000 pp. 225-242.

Higher dimensional Nevanlinna-Pick interpolation theory**Authors**: Ralf Meyer

**Author institution:**SFB 478---Geometrische Strukturen in der Mathematik, Universitaet Munster, Hittorfstr.~27, 48149 Munster, Germany

**Summary:**We compute completely isometric representations of quotients of the operator algebra $\Shift_d$ generated by the $d$-shift introduced by Arveson. This gives rise to a higher dimensional generalization of Nevanlinna-Pick interpolation theory. Quotients of $\Shift_d$ of dimension~$r$ admit a completely isometric representation by \Mp{r\times r}matrices. There is an efficient criterion to decide whether an \Mp{r}dimensional algebra of \Mp{r\times r}matrices is a quotient of $\Shift_d$.

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