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First order differential operators associated to the space of meta-anti-analytic functions

Abstract:

A space of functions is associated with differential operator if the operator transforms the space into itself. This paper shows the construction of all first-order operators with complex coefficients that are associated with the meta-anti-analytic function space. Such construction was possible by obtaining necessary and sufficient conditions on the coefficients of the first order complex differential operator. Application of this research is aimed to find solutions to initials values problems involving space and operators associated with each other.