Abstract
In this paper we shall show that each ƒϵ L p[0,1] (1 ⩽ p ⩽ ∞) has a best L p approximation from the set of exponential sums, V n ( S), provided S is closed. Here V n ( S) denotes the set of all solutions of all n-th order linear homogeneous differential equations with constant coefficients for which the roots of the corresponding characteristic polynomial all lie in S. We thus extend the previously known existence theorems which apply only in the special cases where S is compact or where S= R .
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