On 3D Riesz Systems of Harmonic Conjugates
Speaker:Prof. João Pedro Morias
Institute of Applied Analysis
TU Bergakademie Freiberg, Germary
Date & Time:18 Oct 2012 (Thursday) 10:30
Venue:J216
Organized by:Department of Mathematics

Abstract

In continuation of [1], we discuss two constructive approaches for the generation of harmonic conjugates to find null solutions to the Riesz system in R³. This class of solutions coincides with the subclass of monogenic functions with values in the reduced quaternions. Our first algorithm for harmonic conjugates is based on special systems of homogeneous harmonic and monogenic polynomials, while the second one is presented by means of an integral representation. Some examples of function spaces illustrating the techniques involved are given. More specifically, we discuss the (monogenic) Hardy and weighted Bergman spaces on the unit ball in R³ consisting of functions with values in the reduced quaternions. We end up proving the boundedness of the underlying harmonic conjugation operators in certain weighted spaces.

Joint work with K. Avetisyan and K. Gürlebeck.

Biography

Prof. João Pedro Morias is currently a Postdoctoral Researcher at the Institute of Applied Analysis of TU Freiberg, Germany, as well as, at the Department of Mathematics of University of Aveiro. He obtained his Doctor degree in Mathematics at Bauhaus University Weimar in Germany. Besides, Prof. Morias is also a member of the Editorial Board of Journal: Clifford Analysis, Clifford Algebras and their applications (CACAA) www.cliffordanalysis.com. He is interested in Clifford analysis, Quaternion analysis, Initial-boundary value problems of partial differential equations, Function spaces, Quasiconformal geometry. His publications includes, On monogenic primitives of Fueter polynomials, On the calculation of monogenic primitives, Bohr's Theorem for monogenic functions, Hadamard's real part theorem for monogenic functions Bohr type theorem for monogenic power series etc.