The Local de Branges-Rovnyak Construction and Complete Nevanlinna-Pick Kernels

Scott McCullough
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Scott McCullough: University of Florida, Department of Mathematics

A chapter in Algebraic Methods in Operator Theory, 1994, pp 15-24 from Springer

Abstract: Abstract The purpose of this paper is to characterize finite dimensional complete Nevanlinna-Pick interpolation kernels. This result complements a recent result of Agler [2] and the characterization of finite dimensional Caratheodory interpolation kernels in [8]. Peter Quiggin has also shown that the condition is sufficient for scalar valued interpolation [12]. Further, an abstract finite dimensional version of the de Branges-Rovnyak construction is presented. This construction generalizes versions of the de Branges-Rovnyak construction [7] used by a number of authors, including Agler [5] and Muller [9] for weighted shifts (diagonal kernels) satisfying various polynomial identities.

Date: 1994
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DOI: 10.1007/978-1-4612-0255-4_3

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