**E. Obolashvili**

## Generalized Holomorphic Functions and Clifford Analysis

**abstract:**

With the help of a Clifford Algebra and The Dirac operator, in the multidimensional
space a generalized Cauchy--Riemann system is constructed whose Cauchy-kernel
can be represented explicitely. In the two-dimensional case it is a classical
system and can be considered as Maxwell or Dirac stationary equations with two
independent variables. A classification of Beltrami type equations is given
determined by
elements of the Clifford algebra. Some boundary value problems are
studied.

**Mathematics Subject Classification:**
35J02, 35J25, 35J40, 35J65.

**Key words and phrases:**
Generalized holomorphic functions, Dirac operator,
hyperbolic and elliptic Beltrami equations, Cauchy-kernel,
characteristic form, Riemann--Hilbert problem.