On Surjectivity of Invariant Differential Operators

TL;DR

This paper proves that non-zero invariant differential operators on certain symmetric spaces are surjective on distributions by establishing a topological Paley-Wiener theorem, extending classical harmonic analysis results.

Contribution

It introduces a topological Paley-Wiener theorem for Riemannian symmetric spaces of non-compact type, demonstrating surjectivity of invariant differential operators.

Findings

Invariant differential operators are surjective on distributions.

Established a topological Paley-Wiener theorem for symmetric spaces.

Extended classical harmonic analysis results to non-compact symmetric spaces.

Abstract

By proving a topological Paley-Wiener Theorem for Riemannian symmetric spaces of non-compact type, we show that a non-zero invariant differential operator is a homeomorphism from the space of test functions onto its image and hence surjective when extended to the space of distributions.