Radon transforms and spectral rigidity on the complex quadrics and the real Grassmannians of rank two.
In this work we consider two partial differential operators, define a generalized Radon transform and its dual associated with these operators and characterize its range.
In this paper we study the Radon transform on the set of horocycles of a homogeneous tree , and describe its image on various function spaces. We show that the functions of compact support on that satisfy two explicit Radon conditions constitute the image under of functions of finite support on . We extend these results to spaces of functions with suitable decay on , whose image under satisfies corresponding decay conditions and contains distributions on that are not defined pointwise....