Radon Inversion Formulas over Local Fields
نویسنده
چکیده
Let F be a local field and n ≥ 2 an integer. We study the Radon transform as an operator M : C+ → 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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