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 $\mathcal S_d$ generated by the $d$-shift introduced by Arveson. This gives rise to a higher dimensional generalization of Nevanlinna-Pick interpolation theory. Quotients of $\mathcal S_d$ of dimension $r$ admit a completely isometric representation by ${r\times r}$ matrices. There is an efficient criterion to decide whether an ${r}$-dimensional algebra of ${r\times r}$ matrices is a quotient of $\mathcal S_d$.

Keywords: Dilation theory, ${d}$-contractions, Nevanlinna-Pick interpolation theory interpolation theory

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