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.
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.
