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

In: Algebraic Methods in Operator Theory

Author

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  • Scott McCullough

    (University of Florida, Department of Mathematics)

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.

Suggested Citation

  • Scott McCullough, 1994. "The Local de Branges-Rovnyak Construction and Complete Nevanlinna-Pick Kernels," Springer Books, in: Raúl E. Curto & Palle E. T. Jørgensen (ed.), Algebraic Methods in Operator Theory, pages 15-24, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0255-4_3
    DOI: 10.1007/978-1-4612-0255-4_3
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