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Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L2 metric: Jackson's type direct theorems

Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis... We use the methods of Fourier–Jacobi harmonic analysis to study problems of the approximation of functions in weighted function spaces on the half-axis . We prove analogues of Jackson's direct theorem for the moduli of smoothness of all orders constructed on the basis of Jacobi generalized translations. As a tool for approximation, we use functions with bounded spectrum. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Integral Transforms and Special Functions Taylor & Francis

Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L2 metric: Jackson's type direct theorems

Integral Transforms and Special Functions , Volume 30 (4): 18 – Apr 3, 2019

Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L2 metric: Jackson's type direct theorems

Integral Transforms and Special Functions , Volume 30 (4): 18 – Apr 3, 2019

Abstract

We use the methods of Fourier–Jacobi harmonic analysis to study problems of the approximation of functions in weighted function spaces on the half-axis . We prove analogues of Jackson's direct theorem for the moduli of smoothness of all orders constructed on the basis of Jacobi generalized translations. As a tool for approximation, we use functions with bounded spectrum.

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References (19)

Publisher
Taylor & Francis
Copyright
© 2018 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1476-8291
eISSN
1065-2469
DOI
10.1080/10652469.2018.1562449
Publisher site
See Article on Publisher Site

Abstract

We use the methods of Fourier–Jacobi harmonic analysis to study problems of the approximation of functions in weighted function spaces on the half-axis . We prove analogues of Jackson's direct theorem for the moduli of smoothness of all orders constructed on the basis of Jacobi generalized translations. As a tool for approximation, we use functions with bounded spectrum.

Journal

Integral Transforms and Special FunctionsTaylor & Francis

Published: Apr 3, 2019

Keywords: Fourier–Jacobi harmonic analysis; approximation of functions; generalized moduli of smoothness; Jacobi generalized translation; Jackson type theorems; 33C45; 41A17; 44A20

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