This is an announcement for the paper "Functions with prescribed best linear approximations" by P. L. Combettes and N. N. Reyes.
Abstract: A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions to such problems. A finite family of subspaces is said to satisfy the \emph{Inverse Best Approximation Property (IBAP)} if there exists a point that admits any selection of points from these subspaces as best approximations. We provide various characterizations of the IBAP in terms of the geometry of the subspaces. Connections between the IBAP and the linear convergence rate of the periodic projection algorithm for solving the underlying affine feasibility problem are also established. The results are applied to problems in harmonic analysis, integral equations, signal theory, and wavelet frames.
Archive classification: math.FA
Mathematics Subject Classification: 41A50, 41A65, 65T60
The source file(s), arxiv1.tex: 79105 bytes, is(are) stored in gzipped form as 0905.3520.gz with size 21kb. The corresponding postcript file has gzipped size 162kb.
Submitted from: plc@math.jussieu.fr
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