Weakly sufficient sets for A-∞(D)
Khôi, Le Hai (Institute of Information Technology (Vietnam))
Thomas, Pascal J. (Université Paul Sabatier. Laboratoire Emile Picard)

Date:	1998
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.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Publicacions matemàtiques, V. 42 n. 2 (1998) p. 435-448, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/37945
DOI: 10.5565/PUBLMAT_42298_10

14 p, 158.5 KB

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