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Second Order Differential Operators Associated to the Space of Holomorphic Functions

Abstract:

Let ℱ be a given differential operator, then a function space X is called an associated space to ℱ if ℱ transforms X into itself. In this work we show the construction of all operators of second order with complex coefficients that are associated with the space of holomorphic functions. As an application the solvability of initial value problems involving these operators is shown.