Abstract
In this paper, we continue our research on characterizing the order of linear approximation schemes from shift-invariant spaces, which was started in [4]. Our extension of earlier results applies to various aspects: Firstly, in the definition of the operators we allow more general functions, viz. distributions of finite order. Secondly, we consider the non-stationary case, where the operators may depend on the scaling parameter. Thirdly, we bound the error for derivatives as well, i.e., we can bound the error of simultaneous approximation. Finally, we derive a characterization of the full norm approximation order in addition to the usual seminorm approximation order. Our results are applied to the following examples: Thin-plate splines, multiquadrics, and four-directional box splines.
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Conferenza tenuta da K. Jetter il 5 ottobre 1995
The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from Academia Sinica.
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Jetter, K., Zhon, DX. Seminorm and full norm order of linear approximation from shift-invariant spaces. Seminario Mat. e. Fis. di Milano 65, 277–302 (1995). https://doi.org/10.1007/BF02925261
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DOI: https://doi.org/10.1007/BF02925261