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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Optimal approximation in Hilbert spaces with reproducing kernel functions

Author: F. M. Larkin
Journal: Math. Comp. 24 (1970), 911-921
MSC: Primary 65.20; Secondary 41.00
MathSciNet review: 0285086
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Abstract: Characterisations of optimal linear estimation rules are given in terms of the reproducing kernel function of a suitable Hilbert space. The results are illustrated by means of three different, useful function spaces, showing, among other things, how Gaussian quadrature rules, and the Whittaker Cardinal Function, relate to optimal linear estimation rules in particular spaces.

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Keywords: Optimal approximation, reproducing kernel functions, Gaussian quadrature, optimal quadrature, Szegö kernel, Paley-Wiener-Hilbert space, Whittaker cardinal function
Article copyright: © Copyright 1970 American Mathematical Society