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

Bonet, 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 -