New perspectives in hyperbolic function theory

In this thesis we are working with a function theory on the hyperbolic upper-half space. The function theory is called the hyperbolic function theory and it is studied since 1990's by Heinz Leutwiler and Sirkka-Liisa Eriksson. The advantage of the hyperbolic function theory is that positive and negative powers of hypercomplex variables are included to the theory. Thus the hyperbolic function theory offers a natural generalization of classical complex analysis