# Weakly sufficient sets for A-∞(D).

Publicacions Matemàtiques (1998)

- Volume: 42, Issue: 2, page 435-448
- ISSN: 0214-1493

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topKhôi, 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 -

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