A decrease in growth of Lebesgue constants

E. Liflyand

doi:10.1006/jmaa.1997.5432

A decrease in growth of Lebesgue constants

E. Liflyand

Department of Mathematics

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

3 Scopus citations

Abstract

The Lebesgue constants of cubic partial sums of order N of n-dimensional Fourier series behave asymptotically as lnⁿ N. For cubic linear means generated by a function vanishing only at 2ⁿ corner points the order of growth of the Lebesgue constants decreases and equals asymptotically to ln^n-1 N. This generalizes Kivinukk's results where the ordinary estimates were given.

Original language	English
Pages (from-to)	20-29
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	212
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.1997.5432
State	Published - 1 Aug 1997

Bibliographical note

Funding Information:
* The author acknowledges the support of the Minerva Foundation in Germany through the Emmy Noether Mathematics Institute in Bar-Ilan University. E-mail address: liflyand @macs.biu.ac.il.

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10.1006/jmaa.1997.5432

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abstract = "The Lebesgue constants of cubic partial sums of order N of n-dimensional Fourier series behave asymptotically as lnn N. For cubic linear means generated by a function vanishing only at 2n corner points the order of growth of the Lebesgue constants decreases and equals asymptotically to lnn-1 N. This generalizes Kivinukk's results where the ordinary estimates were given.",

author = "E. Liflyand",

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AB - The Lebesgue constants of cubic partial sums of order N of n-dimensional Fourier series behave asymptotically as lnn N. For cubic linear means generated by a function vanishing only at 2n corner points the order of growth of the Lebesgue constants decreases and equals asymptotically to lnn-1 N. This generalizes Kivinukk's results where the ordinary estimates were given.

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A decrease in growth of Lebesgue constants

Abstract

Bibliographical note

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