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We deal with weighted spaces and HV(U) of holomorphic functions defined on a balanced open subset U of a Banach space X. We give conditions on the weights to ensure that the weighted spaces of m-homogeneous polynomials constitute a Schauder decomposition for them. As an application, we study their reflexivity. We also study the existence of a predual. Several examples are provided.
A method for solving second order matrix differential equations avoiding the increase of the dimension of the problem is presented. Explicit approximate solutions and an error bound of them in terms of data are given.
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