Optimal recovery of interpolation operators in Hardy spaces

Author： Cavaretta A.   Sharma A.  

Publisher： Springer Publishing Company

ISSN： 1019-7168

Source： Advances in Computational Mathematics, Vol.24, Iss.1-4, 2006-01, pp. : 131-141

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Abstract

We continue studies begun by C.A. Micchelli and T.J. Rivlin on optimal recovery in Hp spaces. The feature operators are various interpolation operators drawn from the theory of Walsh equiconvergence, as are the information sets. The theory is of interest in that it identifies linear algorithms which might not otherwise be isolated for study or used as approximations of the feature operators. In some cases, we can identify the optimal algorithm although we cannot explicitly determine the exact order of the approximation that it achieves.

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