The Brenner-Hochster-Koll\'ar and Whitney Problems for Vector-valued Functions and Jets

TL;DR

This paper introduces analytic techniques to find smooth solutions to systems of linear equations and addresses a generalized Whitney problem for vector-valued functions and jets, advancing the understanding of smooth function extension and solution existence.

Contribution

It provides new analytic methods for solving linear systems with smooth solutions and extends Whitney's problem to vector-valued functions and jets, offering novel insights.

Findings

Developed methods for finding m-times differentiable solutions to linear systems.

Solved a generalized Whitney problem for vector-valued functions and jets.

Enhanced understanding of smooth function extension problems.

Abstract

In this paper, we give analytic methods for finding m (and m+\omega) times continuously differentiable solutions of a finite system of linear equations. Along the way, we also solve a generalized Whitney problem for vector-valued functions and jets.