Optimal Recovery of Holomorphic Functions from Inaccurate Information about Radial Integration

• 作者: Arthur DeGraw
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: APPROXIMATION OPTIMAL RECOVERY HOLOMORPHIC
• 年，卷（期）: 2012,（4）
• 页码范围: 258-268
• 页数: 11页
• 分类号: O1

摘要

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.