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On the Jackson–Stechkin Theorems for the Best Approximations of Functions in Clifford Algebras

On the Jackson–Stechkin Theorems for the Best Approximations of Functions in Clifford Algebras In this research, we look at problems in the theory of approximation of functions in real Clifford algebras. We prove analogues of direct and inverse approximation theorems in terms of best approximations of functions with bounded spectrum and the moduli of smoothness of all orders constructed by the generalized Steklov operators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

On the Jackson–Stechkin Theorems for the Best Approximations of Functions in Clifford Algebras

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References (42)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0188-7009
eISSN
1661-4909
DOI
10.1007/s00006-023-01261-3
Publisher site
See Article on Publisher Site

Abstract

In this research, we look at problems in the theory of approximation of functions in real Clifford algebras. We prove analogues of direct and inverse approximation theorems in terms of best approximations of functions with bounded spectrum and the moduli of smoothness of all orders constructed by the generalized Steklov operators.

Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Feb 1, 2023

Keywords: Clifford algebras; Clifford–Fourier transform; Best approximations; Steklov operators; Bernstein’s theorem; Jackson’s theorems; Stechkin’s theorems; Modulus of smoothness; 42B10; 42A38; 43A62

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