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

José Bonet; Reinhold Meise; Sergej N. Melikhov

Publicacions Matemàtiques (2005)

- Volume: 49, Issue: 2, page 487-509
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topBonet, José, Meise, Reinhold, and Melikhov, Sergej N.. "The dual of the space of holomorphic functions on locally closed convex sets.." Publicacions Matemàtiques 49.2 (2005): 487-509. <http://eudml.org/doc/41576>.

@article{Bonet2005,

abstract = {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 CN, 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.},

author = {Bonet, José, Meise, Reinhold, Melikhov, Sergej N.},

journal = {Publicacions Matemàtiques},

keywords = {Espacios de funciones lineales; Espacios de funciones holomorfas; Espacio dual; Espacios de Fréchet; Límite inductivo; space of holomorphic germs; projective description; Laplace transform; multiplication operator; convolution operator; surjectivity},

language = {eng},

number = {2},

pages = {487-509},

title = {The dual of the space of holomorphic functions on locally closed convex sets.},

url = {http://eudml.org/doc/41576},

volume = {49},

year = {2005},

}

TY - JOUR

AU - Bonet, José

AU - Meise, Reinhold

AU - Melikhov, Sergej N.

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

JO - Publicacions Matemàtiques

PY - 2005

VL - 49

IS - 2

SP - 487

EP - 509

AB - 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 CN, 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.

LA - eng

KW - Espacios de funciones lineales; Espacios de funciones holomorfas; Espacio dual; Espacios de Fréchet; Límite inductivo; space of holomorphic germs; projective description; Laplace transform; multiplication operator; convolution operator; surjectivity

UR - http://eudml.org/doc/41576

ER -