Optimal Recovery of Holomorphic Functions from Inaccurate Information about Radial Integration

Arthur DeGraw

Department of Mathematics and Statistics, State University of New York at Albany, Albany, USA.

DOI: 10.4236/ajcm.2012.24035                

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 l₂^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.

Keywords

Approximation; Optimal Recovery; Holomorphic

Conflicts of Interest

The authors declare no conflicts of interest.

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