PreprintCC BY 4.0arXiv
Spherical harmonics with maximal Lp norm growth
Abstract
In this paper, we show that for every p>2, there is an orthonormal basis of spherical harmonics on Sn with n>=2 which achieves the maximal Lp norm growth. More precisely, one basis achieves this growth for all p<=2(n+1)/(n-1), and another for all p>=2(n+1)/(n-1). This extends the results in Han (arXiv:1404.5016) to all dimensions and all p>2, and improves the positive density subsequence there to a whole basis.
Related
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- The non-spherical sup-norm problem for GL(n) and generalized spherical functions
BibTeX
@misc{han2026spherical,
title = {{Spherical harmonics with maximal Lp norm growth}},
author = {Xiaolong Han},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14023},
eprint = {2609.14023},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14023},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spherical harmonics with maximal Lp norm growth
AU - Xiaolong Han
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.14023
UR - https://arxiv.org/abs/2609.14023
AB - In this paper, we show that for every p>2, there is an orthonormal basis of spherical harmonics on Sn with n>=2 which achieves the maximal Lp norm growth. More precisely, one basis achieves this growth for all p<=2(n+1)/(n-1), and another for all p>=2(n+1)/(n-1). This extends the results in Han (arXiv:1404.5016) to all dimensions and all p>2, and improves the positive density subsequence there to a whole basis.
ER -