Approximation via Hausdorff operators

Alberto Debernardi, Elijah Liflyand

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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 languageEnglish
Pages (from-to)512-529
Number of pages18
JournalCanadian Mathematical Bulletin
Volume64
Issue number3
DOIs
StatePublished - 13 Aug 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Canadian Mathematical Society 2020.

Funding

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

FundersFunder number
European Research Council713927
Israel Science Foundation447/16

    Keywords

    • Approximation in Lebesgue spaces
    • Hausdorff operators
    • Moduli of continuity

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