Weakly sufficient sets for A-∞(D).

Khôi, Lê Hai, and Thomas, Pascal J.. "Weakly sufficient sets for A-∞(D).." Publicacions Matemàtiques 42.2 (1998): 435-448. <http://eudml.org/doc/41345>.

@article{Khôi1998,
abstract = {In the space A-∞(D) of functions of polynomial growth, weakly sufficient sets are those such that the topology induced by restriction to the set coincides with the topology of the original space. Horowitz, Korenblum and Pinchuk defined sampling sets for A-∞(D) as those such that the restriction of a function to the set determines the type of growth of the function. We show that sampling sets are always weakly sufficient, that weakly sufficient sets are always of uniqueness, and provide examples of discrete sets that show that the converse implications do not hold.},
author = {Khôi, Lê Hai, Thomas, Pascal J.},
journal = {Publicacions Matemàtiques},
keywords = {Espacios de funciones holomorfas; Factores de crecimiento; Conjuntos; Muestreo; Unicidad},
language = {eng},
number = {2},
pages = {435-448},
title = {Weakly sufficient sets for A-∞(D).},
url = {http://eudml.org/doc/41345},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Khôi, Lê Hai
AU - Thomas, Pascal J.
TI - Weakly sufficient sets for A-∞(D).
JO - Publicacions Matemàtiques
PY - 1998
VL - 42
IS - 2
SP - 435
EP - 448
AB - In the space A-∞(D) of functions of polynomial growth, weakly sufficient sets are those such that the topology induced by restriction to the set coincides with the topology of the original space. Horowitz, Korenblum and Pinchuk defined sampling sets for A-∞(D) as those such that the restriction of a function to the set determines the type of growth of the function. We show that sampling sets are always weakly sufficient, that weakly sufficient sets are always of uniqueness, and provide examples of discrete sets that show that the converse implications do not hold.
LA - eng
KW - Espacios de funciones holomorfas; Factores de crecimiento; Conjuntos; Muestreo; Unicidad
UR - http://eudml.org/doc/41345
ER -