Approximation via Hausdorff operators

Alberto Debernardi; Elijah Liflyand

doi:10.4153/S0008439520000612

Approximation via Hausdorff operators

Alberto Debernardi, Elijah Liflyand

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate functions and the adjoint to that Hausdorff operator of the given function. We find estimates for the rate of approximation in various metrics in terms of the parameter of truncation and the components of the Hausdorff operator. Explicit rates of approximation of functions and comparison with approximate identities are given in the case of continuous functions from the class.

Original language	English
Pages (from-to)	512-529
Number of pages	18
Journal	Canadian Mathematical Bulletin
Volume	64
Issue number	3
DOIs	https://doi.org/10.4153/S0008439520000612
State	Published - 13 Aug 2020
Externally published	Yes

Bibliographical note

Funding Information:
Alberto Debernardi was supported by the ERC starting grant No. 713927 and the ISF grant No. 447/16. Elijah Liflyand is the corresponding author.

Publisher Copyright:
© Canadian Mathematical Society 2020.

Keywords

Approximation in Lebesgue spaces
Hausdorff operators
Moduli of continuity

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10.4153/S0008439520000612

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Approximation via Hausdorff operators

Abstract

Bibliographical note

Keywords

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