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Complex Analysis and Operator Theory

, Volume 12, Issue 4, pp 869–876 | Cite as

On a Local Darlington Synthesis Problem

  • L. Golinskii
Article
  • 50 Downloads

Abstract

The Darlington synthesis problem (in the scalar case) is a problem of embedding a given contractive analytic function to an inner \(2\times 2\) matrix function as an entry. A fundamental result of Arov–Douglas–Helton relates this algebraic property to a purely analytic one known as a pseudocontinuation of bounded type. We suggest a local version of the Darlington synthesis problem and prove a local analog of the ADH theorem.

Keywords

Darlington synthesis Pseudocontinuation Inner matrix function Unitary matrix Nevanlinna Schur and Smirnov classes 

Mathematics Subject Classification

30H05 30H15 30C80 

Notes

Acknowledgements

I thank the participants of the Analysis Seminar at Kharkiv National University for valuable discussions.

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.B. Verkin Institute for Low Temperature Physics and EngineeringKharkovUkraine

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