Second Order Complex and Hyperbolic Differential Operators

Abstract

It is well known that complex holomorphic functions are tightly related with harmonic functions of two real variables, a fact that proved to be of crucial importance for the theories of both classes of functions. On the general level, the same occurs with hyperholomorphic (synonymously - monogenic, regular) functions of (real) Clifford analysis and the harmonic functions of the respective number of (real) variables. By this reason, both one complex variable theory and Clifford analysis are considered as refinements of the corresponding harmonic function theories. This relation is due to the following factorizations of the respective Laplace operators.