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Optimal Recovery of Holomorphic Functions from Inaccurate Information about Radial Integration
Department of Mathematics and Statistics, State University of New York at Albany, Albany, USA
- 1 Department of Mathematics and Statistics, State University of New York at Albany, Albany, USA
American Journal of Computational Mathematics·Volume 02 (2012)·Pages 258–268·Published 18 December 2012·DOI10.4236/ajcm.2012.24035
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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 L 2 norm is bound by δ＞0 or for a finite number of terms the error in l 2 N norm is bound by δ＞0 or lastly the error in the j th coefficient is bound by δ j ＞0. The results are applied to the Hardy-Sobolev and Bergman-Sobolev spaces.
KeywordsApproximationOptimal RecoveryHolomorphic
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