On a Local Darlington Synthesis Problem
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.
KeywordsDarlington synthesis Pseudocontinuation Inner matrix function Unitary matrix Nevanlinna Schur and Smirnov classes
Mathematics Subject Classification30H05 30H15 30C80
I thank the participants of the Analysis Seminar at Kharkiv National University for valuable discussions.