The inverse Radon transform and the fundamental solution of the hyperbolic Dirac equation (Q1762719)

The paper is organised as follows: Section 1, Introduction, describes rather briefly a motivation of the topic. Section 2, Hyperbolic Spaces, presents a model for the \(m\)-dimensional hyperbolic unit ball which is used in what follows. Section 3, The Clifford Setting, is a brief overview of Clifford algebras and Clifford analysis. Section 4, The Radon Transform, prepares the main tools allowing then, in Section 5, Reduction of the Dirac equation to a 2-dimensional problem, and Section 6, The Fundamental Solution of the hyperbolic Dirac equations, to obtain a formula for the hyperbolic fundamental solution which is found, in case of \(m\geq3\), as a modulated version of the Euclidean fundamental solution; here \(m\) is the dimension of the underlying space of Clifford algebra.