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A note on a theorem of Stanton-Weinstein on the L4-norm of spherical harmonics

Published online by Cambridge University Press:  24 October 2008

Jiang-Hua Lu
Jiang-Hua Lu
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A.
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Extract

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 .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 3 , November 1987 , pp. 561 - 563
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCE

[1]Stanton, R. J. and Weinstein, A.. On the L 4 norm of spherical harmonics. Math. Proc. Cambridge Philos. Soc. 89 (1981), 343–358.CrossRefGoogle Scholar