Abstract

A continuous complex valued function f=u+iv defined in a simply connected complex domain D is said to be harmonic in D if both u and v are real harmonic in D. Let F and G be analytic in D so that F(0)=G(0)=0, ReF = Ref=u, ReG = Imf=v by writing (F+iG)/2 = h, (FiG)/ 2 = g, The function f admits the representation f = h + g , where h and g are analytic in D. h is called the analytic part of f and g, the co-analytic part of f.