Functional Analysis Holomorphy and Approximation Theory : Proceedings of the Seminário de Análise Funcional Holomorfia e Teoria da Aproximação Universidade Federal do Rio de Janeiro Brazil August 7 – 11 1978 An example of a quasi normable Fréchet function space which is not a Schwartz space The Levi problem and the radius of convergence of holomorphic functions on metric vector spaces Extending nonarchimedean norms on algebras M structure in tensor products of Banach spaces Silva holomorphy types borel transforms and partial differential operators The approximation theoretic locaization of Schwartzs approximation property for weighted locally convex function spaces and some examples An application of Korovkins theorem to certain partial differential equations The fourier borel transform in infinitely many dimensions and applications On the solvability of differential equations of infinite order in non metrizable spaces C functions on locally convex and on bornological vector spaces Uniform measures and CoSaks spaces Holomorphic germs on compact subsets of locally convex spaces Some mathematical problems in non equilibrium statistical mechanics Generalized Hewitt Nachbin spaces arising in state space completions On the topology of compact complex surfaces Jordan algebras and holomorphy How to recognize supports from the growth of functional transforms in real and complex analysis Linear differential operators on vector spaces Solutions Faibles et Solutions Fortes du Problème u=f où f est une Fonction à Croissance Polynomiale sur un Espace de Hilbert Silva holomorphy types Envelopes for types of holomorphy Domains of holomorphy in (DFC) spaces Homomorphisms of algebras of germs of holomorphic functions On the spectra of non archimedean function algebras An example of the barrelled space associated to C(X;E) On suprabarrelled spaces Envelopes of silva holomorphy Dense subalgebras in topological algebras of differentiable functions.