CaltechAUTHORS
  A Caltech Library Service

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. http://resolver.caltech.edu/CaltechAUTHORS:20170621-113817868

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20170621-113817868

Abstract

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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/978-3-319-31281-1_18DOIArticle
https://link.springer.com/chapter/10.1007/978-3-319-31281-1_18PublisherArticle
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.
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-15-1-0385
Record Number:CaltechAUTHORS:20170621-113817868
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170621-113817868
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78417
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Jun 2017 21:30
Last Modified:21 Jun 2017 21:30

Repository Staff Only: item control page