E. Obolashvili

Generalized Holomorphic Functions and Clifford Analysis

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.