Analytic free Maps and structured Non commutative multidimensional linear System

Abstract

We show concerns analytic free maps . These maps are free analogy's of classical analytic functions in several complex variables , and are defined in terms of non – commuting variables amongst which there are no relations – they are free variables . Analytic free maps include variables with the highest degree of non commutatively pose many difficult problems , the free difference quotient We discuss the difference quotient derivation on homorphic functions , in which the component is replaced by a Banach alagebra .