Revistes Catalanes amb Accés Obert (RACO)

Weakly sufficient sets for $A^{-\infty} (\Bbb D)$

L. H. Khôi, P. J. Thomas


In the space $A^{-\infty} (\Bbb D)$ 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 $A^{-\infty} (\Bbb D)$ 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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