Whitney extensions on symmetric spaces

TL;DR

This paper extends Whitney's classical function extension problem to symmetric spaces using harmonic analysis and representation theory, broadening the scope of Whitney extension theorems beyond Euclidean spaces.

Contribution

It establishes Whitney type extension theorems for functions on homogeneous spaces, utilizing harmonic analysis and representation theory of reductive groups.

Findings

Proves Whitney extension theorems on certain symmetric spaces.

Employs harmonic analysis and representation theory techniques.

Extends classical Euclidean results to non-Euclidean homogeneous spaces.

Abstract

In 1934, H. Whitney introduced the problem of extending a function on a set of points in $\mathbb{R}^n$ to an analytic function on the ambient space. In this article we prove Whitney type extension theorems for data on some homogeneous spaces. We use harmonic analysis on the homogeneous spaces and representation theory of compact as well as noncompact reductive groups.