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A. G. Marchuk and K. Y. Osipenko, “Best Approximations of Functions Specified with an Error at a Finite Number of Points,” Mathematical notes of the Academy of Sciences of the USSR, Vol. 17, No. 3, 1975, pp. 207- 212. doi:10.1007/BF01149008

has been cited by the following article:

• TITLE: Optimal Recovery of Holomorphic Functions from Inaccurate Information about Radial Integration

  AUTHORS: Arthur DeGraw

  KEYWORDS: Approximation; Optimal Recovery; Holomorphic

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.2 No.4, December 18, 2012

  ABSTRACT: This paper addresses the optimal recovery of functions from Hilbert spaces of functions on the unit disc. The estimation, or recovery, is performed from inaccurate information given by integration along radial paths. For a holomorphic function expressed as a series, three distinct situations are considered: where the information error in L2 norm is bound by δ＞0 or for a finite number of terms the error in l2N norm is bound by δ＞0 or lastly the error in the jth coefficient is bound by δj＞0. The results are applied to the Hardy-Sobolev and Bergman-Sobolev spaces.