Abstract
One important topic in approximation theory is the approximation by linear operators of convolution type. In many cases of interest the kernels are, for example, integrable functions or bounded measures, thus belong to certain Banach algebras. As the approximation is governed by a detailed study of the kernels, it seems to be natural to look on this section of approximation theory from the point of view of abstract Banach algebras, particularly since the Gelfand transform may be used as a substitute for integral transforms, the most effective tool in the classical setting.
The research of this author was supported by the “Landesamt für Forschung bei dem Minister für Wissenschaft und Forschung des Landes Nordrhein-Westfalen” Grant No. IV A5-5334. Thanks are due to the Landesamt for permission to publish the results in these Proceedings.
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References
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Bragard, G.K., Nessel, R.J. (1974). On the Comparison of Approximation Processes in Banach Algebras. In: Butzer, P.L., Szőkefalvi-Nagy, B. (eds) Linear Operators and Approximation II / Lineare Operatoren und Approximation II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 25. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5991-2_7
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DOI: https://doi.org/10.1007/978-3-0348-5991-2_7
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