Radon inversion formulas over local fields

2015/03/13 by Wang, Jonathan
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1503.04095

Abstract

Let F be a local field and n≥ 2 an integer. We study the Radon transform as an operator M : \mathcal C₊ → \mathcal C_- from the space of smooth K-finite functions on Fⁿ ∖ \0\ with bounded support to the space of smooth K-finite functions on Fⁿ ∖ \0\ supported away from a neighborhood of 0. These spaces naturally arise in the theory of automorphic forms. We prove that M is an isomorphism and provide formulas for M^-1. In the real case, we show that when K-finiteness is dropped from the definitions, the analog of M is not surjective.

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