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The indefinite metric in the Schur interpolation problem for analytic functions. IV

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Topics in Interpolation Theory

Part of the book series: Operator Theory Advances and Applications ((OT,volume 95))

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Abstract

A complete description is given of the set of all contractive matrix valued holomorphic functions in the disc whose first n +1 matrix coefficients in their power series expansion about zero are specified when the associated information block (or Pick matrix) is positive semidefinite and singular. In an earlier part of this series,2 a complete description was given when the associated information block is positive and nonsingular. [Abstract added by editors.]

Translated from: Teor. Funkciĭ, Funkcional. Anal. i Prilozen 42 (1984), 46–57, (The Kharkov University publishing house, Marchenko, V.A., — ed) [MR 86c:47008].

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References

  1. Dubovoj, V.K.: Indefinite metric in the interpolation problem of Schur for analytic matrix functions. I (in Russian), Teor. Funkciĭ, Funkcional. Anal. i Prilozen 37 (1982), 14–26, (The Kharkov University publishing house, Marchenko, V.A. -ed) [MR 85f:30059a]. Engl. Transl. in: Amer. Math. Soc. Transl. (ser. 2) 144 (1989) (Thirteen Papers Translated from Russian), 47–60.

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Dubovoj, V.K. (1997). The indefinite metric in the Schur interpolation problem for analytic functions. IV. In: Dym, H., Katsnelson, V., Fritzsche, B., Kirstein, B. (eds) Topics in Interpolation Theory. Operator Theory Advances and Applications, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8944-5_5

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  • DOI: https://doi.org/10.1007/978-3-0348-8944-5_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9838-6

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