Wolff's Theorem on Ideals for Matrices

TL;DR

This paper extends Wolff's theorem from scalar functions to matrix-valued functions in H-infinity, establishing conditions for the existence of solutions to matrix equations across the unit disk.

Contribution

It introduces a matrix version of Wolff's theorem, providing new conditions for solutions in the H-infinity space for matrix equations.

Findings

Established conditions for matrix solutions in H-infinity

Extended scalar Wolff's theorem to matrices

Analyzed several useful related results

Abstract

We extend Wolff's theorem concerning ideals on H-infinity(D) to the matrix case, giving conditions under which an H-infinity solution G to the equation FG = H exists for all z in D, where F is an m-by-infinity matrix of functions in H-infinity (D), and H is an m-by-1 vector of such functions. We then examine several useful results.