A General Theorem on Lebesgue Constants

E. Liflyand

doi:10.1007/s10958-022-06213-z

A General Theorem on Lebesgue Constants

E. Liflyand

Department of Mathematics

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

Abstract

A very general asymptotic type formula is presented for the Lebesgue constants of both Fourier partial sums and linear methods of summability of Fourier series in the multivariate Euclidean spaces. More precisely, the obtained formula represents the norm of a trigonometric polynomial with coefficients being the values of a multiplier as the norm of the Fourier transform of this multiplier, with an error which in many cases (after appropriate estimates) leads either to a really asymptotic relation or to a suitable upper estimate.

Original language	English
Pages (from-to)	435-442
Number of pages	8
Journal	Journal of Mathematical Sciences
Volume	268
Issue number	4
DOIs	https://doi.org/10.1007/s10958-022-06213-z
State	Published - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022, Springer Science+Business Media, LLC, part of Springer Nature.

Funding

This work is financially supported and performed under the auspices of the Iran National Science Foundation and the University of Tarbiat Modares in the program of postdoctoral research projects.

Funders	Funder number
Iran National Science Foundation
Tarbiat Modares University

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10.1007/s10958-022-06213-z

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A General Theorem on Lebesgue Constants

Abstract

Bibliographical note

Funding

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