2014/07/06 by Vivian M. Ho, Ho, Vivian M., Gestur Ólafsson +1
Mathematics · #22E46 #33C67 #43A85 #43A90 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Representation Theory (math.RT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1407.1489
openalex publication_date 2014/07/06 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Paley-Wiener type theorems describe the image of a given space of functions,\noften compactly supported functions, under an integral transform, usually a\nFourier transform on a group or homogeneous space. Several authors have studied\nPaley-Wiener type theorems for Euclidean spaces, Riemannian symmetric spaces of\ncompact or non-compact type as well as affine Riemannian symmetric spaces. In\nthis article we prove a Paley-Wiener theorem for homogeneous line bundles over\na compact symmetric space U/K. The Paley-Wiener theorem characterizes f with\nsufficiently small support in terms of holomorphic extendability and\nexponential growth of their Fourier transforms. An important tool is a\ngeneralization of Opdam's estimate for the hypergeometric functions for\nmultiplicity functions that are not necessarily positive. The domain where this\nestimate is valid is also bigger. This is done in an appendix.\n