Local error estimation for sampling problems
This paper is motivated by recent work of \textit{N. Atreas, J. J. Benedetto} and \textit{C. Karanikas} [Sampl. Theory Signal Image Process. 2, No. 1, 1--24 (2003; Zbl 1049.42018)] on local sampling for regular wavelet and Gabor expansions. Their result is complicated in form and the method is difficult to generalize to higher dimensional cases. In this paper, a new method to evaluate the decay of the sampling function is given, so it can be used to derive a more subtle local error estimation for the reconstruction formulas in a multiresolution analysis and shift-invariant space.
scientific article; zbMATH DE number 2128781
scientific article