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Multi-Point Degenerate Interpolation Problem for Generalized Schur Functions: Description of All Solutions

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Abstract

We consider the Nevanlinna-Pick-Carathéodory-Fejér interpolation problem with finitely many interpolation conditions in the class Sgk of meromorphic functions f with ∥f∥l∞(t) ≤ 1 and with κ poles inside the unit disk D. The problem has infinitely many solutions if and only if κ is greater than or equal to the number of non-positive eigenvalues (counted with multiplicities) of the Pick matrix P constructed from interpolation data. For each such κ, we describe the solution set of the problem in terms of a family of linearfractional transformations with disjoint ranges. The parameters defining this family are free and independent.

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Authors and Affiliations

  1. Department of Mathematics, The College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Vladimir Bolotnikov

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  1. Vladimir Bolotnikov
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Correspondence to Vladimir Bolotnikov.

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The author was partially supported by National Science Foundation Grant DMS 0901124

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Bolotnikov, V. Multi-Point Degenerate Interpolation Problem for Generalized Schur Functions: Description of All Solutions. Comput. Methods Funct. Theory 11, 143–160 (2011). https://doi.org/10.1007/BF03321794

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