Unbounded Lebesgue constants on compact groups

Christopher Meaney*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let G be a compact group with dual object Γ. A decomposition of Γ into pairwise disjoint finite sets provides a way of defining partial sums of Fourier series on G. We employ a theorem of Olevskii to present a condition on such a decomposition which, if satisfied, guarantees that the corresponding Lebesgue constants are unbounded. We apply this to certain summation methods on tori and compact connected semisimple Lie groups.

Original languageEnglish
Pages (from-to)119-129
Number of pages11
JournalMonatshefte für Mathematik
Volume91
Issue number2
DOIs
Publication statusPublished - Jun 1981
Externally publishedYes

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