On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative


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Authors

  • Sergei Artamonov

DOI:

https://doi.org/10.32523/2077-9879-2018-9-2-11-21

Keywords:

modulus of smoothness, Riesz derivative, K-functional, Bernstein space

Abstract

A new non-periodic modulus of smoothness related to the Riesz derivative is constructed. Its properties are studied in the spaces Lp(ℝ) of non-periodic functions with 1 ≤ p ≤ +∞. The direct Jackson type estimate is proved. It is shown that the introduced modulus is equivalent to the K-functional related to the Riesz derivative and to the approximation error of the convolution integrals generated by the Fejér kernel.

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Published

2018-06-30

How to Cite

Artamonov, S. (2018). On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative. Eurasian Mathematical Journal, 9(2), 11–21. https://doi.org/10.32523/2077-9879-2018-9-2-11-21

Issue

Vol. 9 No. 2 (2018)

Section

Articles

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