10 th Annual Workshop on Applications and Generalizations of Complex Analysis

Supported by: CIM-Centro Internacional de Matemática CMUC-Centro de Matemática da Universidade de Coimbra UIMAUnidade de Investigação Matemática e Aplicações da Universidade de Aveiro 9:45-10:15 Richard Delanghe, University of Ghent Subclasses of monogenic functions Let Ω ⊂ R be open and let R0,m+1 be the real Cli ord algebra generated by the orthonormal basis e = (e0, e1, ..., em) of the quadratic vector space R. Furthermore, let F : Ω→ R0,m+1 be a smooth function in Ω. Then F is said to be left (resp. right) monogenic in Ω i ∂xF = 0 (resp. F∂x = 0) in Ω. Hereby ∂x = ∑m i=0 ei∂xi is the Dirac operator in R. Consider the decomposition of R0,m+1 into its r-vector subspaces R 0,m+1, i.e. R0,m+1 = m+1 ∑