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Bitangential Interpolation in Generalized Schur Classes

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Abstract

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in Derkach and Dym (On linear fractional transformations associated with generalized J-inner matrix functions. Integ Eq Oper Th (2009, in press) arXiv:0901.0193).

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Authors and Affiliations

  1. Department of Mathematics, Donetsk State University, Universitetskaya str. 24, 83055, Donetsk, Ukraine

    Vladimir Derkach

  2. Department of Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Harry Dym

Authors
  1. Vladimir Derkach
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  2. Harry Dym
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Correspondence to Harry Dym.

Additional information

Communicated by Daniel Alpay.

V. Derkach wishes to thank the Weizmann Institute of Science for hospitality and support.

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Derkach, V., Dym, H. Bitangential Interpolation in Generalized Schur Classes. Complex Anal. Oper. Theory 4, 701–765 (2010). https://doi.org/10.1007/s11785-009-0031-3

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