The main purpose of the talk is to study the main properties of the Quaternion Fourier Transform (QFT), the de_nition of distribution in the context of quaternion analysis and its properties. We de_ne the QFT of distributions, and study some of its properties. In addition, we will discuss some further generalizations of the classical BochnerSchwartz, Eppstein and MalgrangeEhrenprais theorems in the framework of quaternion analysis.

Professor Svetlin Georgiev Georgiev received his Ph. D. from Max Planch. He is currently a Professor of Ordinary and Partial Differential Equations and Editor of Mathematical Methods in the Applied Sciences. He is interested in Ordinary, Partial and Stochastic Differential Equations, Mathematical Modeling, Quaternion Analysis and Clifford Analysis. His publications include, New aspects of elementary functions in the context of quaternionic analysis, Local and global existence for a class integro-differential equations with delay, Blow up of the solutions for a class nonlinear wave equations etc.