Silva-holomorphy types, borel transforms and partial differential operators

Abstract

Dineen in [2] described and studied various topological vector spaces of holomorphic functions and introduced the α-holomorphy, α-β-holomorphy and α-β-γ-holomorphy types solving questions about Borel transforms, convolution and partial differential operators. Matos & Nachbin in working with Silva-holomorphic functions between two complex locally spaces defined Silva-holomorphy types ϑ and obtained results about Borel transforms and Malgrange's theorem for convolution operators. In this work, using the techniques developed in [2] and using the study of the Silva-holomorphic functions in complex locally convex spaces, we generalize the results presented by Dineen in [2].