On Surjectivity of Invariant Differential Operators

2010/06/11 by Thomas Hjortgaard Danielsen, Danielsen, Thomas Hjortgaard
Mathematics · Physics and Astronomy · #22E30 #43A85 #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1006.2276

openalex publication_date 2010/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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