Radon-Type Transforms for Holomorphic Functions in the Lie Ball

Abstract

In this paper, we consider holomorphic functions on the m-dimensional Lie ball LB(0, 1) which admit a square integrable extension on the Lie sphere. We then define orthogonal projections of this set onto suitable subsets of functions defined in lower- dimensional spaces to obtain several Radon-type transforms. For all these transforms we provide the kernel and an integral representation, besides other properties. In particular, we introduce and study a generalization to the Lie ball of the Szegő–Radon transform introduced in Colombo et al. (Adv Appl Math 74:1–22, 2016), and various types of Hua–Radon transforms.