Corona Solutions Depending Smoothly on Corona Data

TL;DR

This paper demonstrates that solutions to Bezout equations can be chosen to depend smoothly on parameters if the Corona data does, ensuring consistent smoothness in parameter-dependent solutions.

Contribution

It establishes the smooth dependence of Bezout equation solutions on parameters given smoothly varying Corona data.

Findings

Solutions can be chosen to depend smoothly on parameters.

Smoothness of solutions matches the smoothness of data.

Provides a theoretical foundation for parameter-dependent solutions.

Abstract

In this note we show that if the Corona data depends continuously (smoothly) on a parameter, the solutions of the corresponding Bezout equations can be chosen to have the same smoothness in the parameter.