Lower-dimensional decompositions using complex variables

Wolfgang Tutschke

Address. Technical University Graz, Department of Mathematics, Steyrergasse 30/3, A-8010 Graz, AUSTRIA

E-mail: tutschke@matd.tu.graz.ac.at

Abstract. The purpose of the present paper is to represent non-holomorphic functions depending on one or several complex variables by holomorphic and anti-holomorphic functions depending on only one complex variable. Similarly as in the case of functions of real variables, the obtained criteria can also be interpreted as conditions for the solvability of functional equations.

AMSclassification. 39B32, 30D05, Secondary: 34A20, 30G20

Keywords. Holomorphic solution of functional equations, poly-analytic functions, ordinary differential equations in the complex domain