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Compressed Resolvents, Schur Functions, Nevanlinna Families and Their Transformations

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Abstract

We study certain transformations of Nevanlinna families and Schur class operator-valued functions, construct their realizations by means of compressed resolvents and by the transfer functions of conservative systems, and find fixed points of such transformations. In particular, we characterize some automorphic Schur functions and corresponding them Nevanlinna families, including periodic and scale invariant.

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Acknowledgements

It is my great pleasure to thank referees for their careful reading of the paper, for valuable remarks and suggestions.

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    Yu. M. Arlinskiĭ

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Communicated by Sanne ter Horst, Dmitry S. Kaliuzhnyi-Verbovetskyi and Izchak Lewkowicz.

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This article is part of the topical collection “Linear Operators and Linear Systems” edited by Sanne ter Horst, Dmitry S. Kaliuzhnyi-Verbovetskyi and Izchak Lewkowicz.

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Arlinskiĭ, Y.M. Compressed Resolvents, Schur Functions, Nevanlinna Families and Their Transformations. Complex Anal. Oper. Theory 14, 63 (2020). https://doi.org/10.1007/s11785-020-01019-w

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