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Estimates from below for Lebesgue constants of Fourier series on compact Lie groups

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Abstract

In this paper the Lebesque constants (L KR (G))R>0 of Fourier series on compact Lie groups G corresponding to general one-dimensional groupings on the dual object G^ are estimated from below by the associated (abelian) Lebesgue constants (L KR (T))R>0 on a maximal torus T in G. For spherical groupings this leads to the estimate L ⊙R (G)≧const.R(l-1)/2, l=dimT≧2.

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  1. Fachbereich 6-Mathematik, Gesamthochschule Siegen, Hölderlinstraße 3, D-5900, Siegen 21

    Bernd Dreseler

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  1. Bernd Dreseler
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Dreseler, B. Estimates from below for Lebesgue constants of Fourier series on compact Lie groups. Manuscripta Math 31, 17–23 (1980). https://doi.org/10.1007/BF01303267

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  • DOI: https://doi.org/10.1007/BF01303267

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