Optimal recovery from a finite set in Banach spaces of entire functions

Abstract

We develop an approach to the problem of optimal recovery of continuous linear functionals in Banach spaces through information on a finite number of given functionals. The results obtained are applied to the problem of the best analytic continuation from a finite set in the complex space C n , n ⩾ 1 , for classes of entire functions of exponential type which belong to the space L p , 1 < p < ∞ , on the real subspace of C n . These latter are known as Wiener classes.