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Optimal recovery of interpolation operators in Hardy spaces

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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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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, U.S.A.

    A. S. Cavaretta

  2. University of Alberta, Department of Mathematics, Edmonton, Alberta, T6G 2G1, Canada

    A. Sharma

Authors
  1. A. S. Cavaretta
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  2. A. Sharma
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Corresponding author

Correspondence to A. S. Cavaretta.

Additional information

Communicated by T.N.T. Goodman

For Charles Micchelli on his sixtieth birthday, with appreciation

Mathematics subject classifications (2000)

41A05, 30B30.

A. Sharma: Deceased.

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Cavaretta, A.S., Sharma, A. Optimal recovery of interpolation operators in Hardy spaces. Adv Comput Math 24, 131–141 (2006). https://doi.org/10.1007/s10444-004-4134-0

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  • DOI: https://doi.org/10.1007/s10444-004-4134-0

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