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arXiv · 1806.03727

Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods

Xianghong Chen·Dashan Fan·Juan Zhang
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Abstract

We show that there exists an integrable function on the $n$-sphere $(n\ge 2)$, whose Ces\`aro (C,$\frac{n-1}{2}$) means with respect to the spherical harmonic expansion diverge unboundedly almost everywhere. By studying equivalence theorems, we also obtain the corresponding results for Riesz and Bochner-Riesz means. This extends results of Stein (1961) for flat tori and complements the work of Taibleson (1985) for spheres.

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Xianghong Chen, Dashan Fan, Juan Zhang. 2018-06-10. Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods. https://arxiv.org/abs/1806.03727

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