Judith Vanegas

Associated Operators to the Space of Elliptic Generalized-Analytic Functions

We find all linear first order partial differential operators with elliptic complex numbers-valued coefficients that are associated to an elliptic generalized-analytic operator. As an application, the solvability of initial value problems involving these operators is shown.

A Dirichlet problem for powers of the generalized Cauchy-Riemann operator

Abstract In this paper we solve a Dirichlet problem in ℝ3 for the equation Dnu = 0, where Dn is the n-th power of generalized Cauchy-Riemann operator and u is a Clifford algebra depending on parameters valued function.

Generalized Cauchy-Riemann-type operators and some integral representation formulas

We introduce some generalized Cauchy-Riemann-type operators. For some of them we give integral representation formulas which allow to study boundary value problems involving these operators.