Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1993-06-30
Two-Sided Nevanlinna-Pick Interpolation for a Class of Matrix-Valued FunctionsDaniel Alpay and Vladimir Bolotnikov (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  and by D. Alpay and H. Dym in . 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