Blaschke products and unwinding in higher dimensions
Ronald R. Coifman, Jacques Peyri\`ere
TL;DR
This paper establishes a precise criterion for the convergence of infinite products of rational inner functions on the polydisk and extends concepts like Malmquist-Takenaka bases and unwinding to higher dimensions.
Contribution
It provides a necessary and sufficient condition for convergence and generalizes classical one-dimensional concepts to the multivariable setting.
Findings
Derived a convergence criterion for infinite products of rational inner functions
Extended Malmquist-Takenaka bases to higher dimensions
Explored various versions of unwinding in the polydisk
Abstract
We give a necessary and sufficient condition for the convergence of an infinite product of rational inner functions on the polydisk, and explore generalization to the polydisk of Malmquist- Takenaka bases and various versions of unwinding
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Taxonomy
TopicsHolomorphic and Operator Theory · Meromorphic and Entire Functions · Advanced Banach Space Theory