Generalized Analytic Functions in elliptic complex numbers
In this talk we will introduce a definition of Generalized Analytic Functions
(in the sense of Vekua), in elliptic complex numbers. One advantage of this definition
is that its Canonical Form is more general than Vekua's and in many cases the reduction
from the elliptic and linear partial differential equation of first order can be done
without solving an associated Beltrami equation. Finally, using techniques of Vekua we
will show that these functions satisfy a representation formula that generalizes the
Similarity Principle in the ordinary case.