Study of some properties of analytic functions

1. DEFINITION OF ANALYTIC FUNCTIONS

Reminder. - The field C is an algebra over the field R. The elements 1,i form a basis of C over R.

An analytic function f, may be regarded as a map:  (x,y) →u(x,y) + I v(x,y)  =f(x, y), from R²  into the algebra C, such that, such that,

^iD_x^{f  - D}_y^{f = (iD}_x ^{- D}_y^{) f = 0}

This formula remains meaningful when is a distribution

Thesis work submitted to the Faculty of the Groduate School of the University of Maryland in partial fulfillment of the requirement for the degree of Master of Arts, 7963.