Abstract
In this paper, we continue the investigations initiated in [1, 2]. Our concern is to identify Banach spaces of holomorphic functions for which sampling of function values yields optimal information in the following sense. Let B be a Banach space of holomorphic functions on a domain D in the complex plane with norm N' HnLet X be another Banach space of complex-valued functions with norm ]j 9 )l x and assume that B = X. We wish to estimate, in the norm of X, an element f of B by means of n linear observations L1 ... . . L, ~ B*. We accomplish this by choosing an algorithm A, that is, a mapping A : C " ~ X , and use A(L l f , .... L , f ) as an approximation of f. The error for A, given only that f ~ B, is
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