A note on a theorem of Stanton-Weinstein on the L4-norm of spherical harmonics
Jiang-Hua Lu · Mathematical Proceedings of the Cambridge Philosophical Society · 1987
1. Let El (l = 0,1,2, …) be the eigenspaces of the Laplacian on the standard 2-sphere S2. Consider the function r2. 4: El −{0} → R given by Stanton and Weinstein proved in [1] that r2, 4 was locally maximized by the ‘highest weight’ function . This note is to simplify part of their proof, namely that of the negativity of .