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Localized Summability Kernels for Jacobi Expansions

Mhaskar, H. N. (2016) Localized Summability Kernels for Jacobi Expansions. In: Mathematical Analysis, Approximation Theory and Their Applications. Springer Optimization and Its Applications. Vol.111. No.111. Springer , Cham, Switzerland, pp. 417-434. ISBN 978-3-319-31279-8.

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While the direct and converse theorems of approximation theory enable us to characterize the smoothness of a function f:[−1,1] → R in terms of its degree of polynomial approximation, they do not account for local smoothness. The use of localized summability kernels leads to a wavelet-like representation, using the Fourier–Jacobi coefficients of f, so as to characterize the smoothness of f in a neighborhood of each point in terms of the behavior of the terms of this representation. In this paper, we study the localization properties of a class of kernels, which have explicit forms in the “space domain,” and establish explicit bounds on the Lebesgue constants on the summability kernels corresponding to some of these.

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Additional Information:© 2016 Springer International Publishing Switzerland. The research of the author is supported in part by Grant W911NF-15-1-0385 from the U.S. Army Research Office. The author thanks Dr. Frank Filbir for many helpful discussions.
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-15-1-0385
Series Name:Springer Optimization and Its Applications
Issue or Number:111
Record Number:CaltechAUTHORS:20170621-113817868
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78417
Deposited By: Ruth Sustaita
Deposited On:21 Jun 2017 21:30
Last Modified:03 Oct 2019 18:08

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