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Zeitschrift für Analysis und ihre Anwendungen

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Volume 12, Issue 2, 1993, pp. 211–238
DOI: 10.4171/ZAA/570

Published online: 1993-06-30

Two-Sided Nevanlinna-Pick Interpolation for a Class of Matrix-Valued Functions

Daniel Alpay[1] and Vladimir Bolotnikov[2]

(1) Ben Gurion University of the Negev, Beer Sheva, Israel
(2) College of William and Mary, Williamsburg, USA

Families of Matrix-valued analytic functions $W(\rho, P)$ depending on two parameters $\rho$ and $P$ are introduced. These include as special cases the Schur and Carathéodory functions, as well as classes of functions studied by the authors in [1] and by D. Alpay and H. Dym in [6]. A two sided Nevanlinna-Pick interpolation problem is defined and solved in $W(\rho, P)$, using the fundamental matrix inequality method.

Keywords: Nevanlinna-Pick interpolation, reproducing kernel spaces, fundamental matrix inequalities

Alpay Daniel, Bolotnikov Vladimir: Two-Sided Nevanlinna-Pick Interpolation for a Class of Matrix-Valued Functions. Z. Anal. Anwend. 12 (1993), 211-238. doi: 10.4171/ZAA/570