2000/05/19 by Anton Deitmar, Deitmar, Anton
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #math.AP
paper · pdf · doi:10.48550/arxiv.math/0005190
Latex, 11 pages
arxiv created 2000/05/19 · openalex publication_date 2000/05/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with respect to the larger algebra of all invariant operators. We compute the possible eigencharacters and show that for invariant integral operators the eigencharacter is given by the Abel transform. We show that sufficiently regular operators are surjective, i.e. that equations of the form Df=u are solvable for all u.