The dual of the space of holomorphic functions on locally closed convex sets

Autores: S.N. Melikhov, Reinhold Meise , José Antonio Bonet Solves
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 49, Nº 2, 2005, págs. 487-509
Idioma: inglés
DOI: 10.5565/publmat_49205_12
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Resumen
- Let $H(Q)$ be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset~$Q$ of $\mathbb{C}^N$, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual $H(Q)'$ of $H(Q)$ can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.