Spherical harmonics with maximal Lp (2<p<=6) norm growth
Classical Analysis and ODEs
2014-04-22 v1 Spectral Theory
Abstract
In this paper, we show that there exists a positive density subsequence of orthonormal spherical harmonics which achieves the maximal Lp norm growth for 2<p<=6, therefore giving an example of a Riemannian surface supporting such subsequence of eigenfunctions. This answers the question proposed by Sogge and Zelditch (arXiv:1011.0215). Furthermore, we provide an explicit lower bound on the density in this example.
Cite
@article{arxiv.1404.5016,
title = {Spherical harmonics with maximal Lp (2<p<=6) norm growth},
author = {Xiaolong Han},
journal= {arXiv preprint arXiv:1404.5016},
year = {2014}
}
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15 pages