Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-06-17T17:33:20.085Z Has data issue: false hasContentIssue false
  • English
  • Français

On the L4 norm of spherical harmonics

Published online by Cambridge University Press:  24 October 2008

Robert J. Stanton  and
Alan Weinstein
Robert J. Stanton
Affiliation:
Rice University, Texas and University of California at Berkeley
Alan Weinstein
Affiliation:
Rice University, Texas and University of California at Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that, among all the L2 normalized spherical harmonics of a given degree, the L4 norm is locally maximized by the ‘highest weight’ function .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 343 - 358
Copyright
Copyright © Cambridge Philosophical Society 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

(1)Bohm, D.Quantum Theory (Prentice-Hall, New York, 1951).Google Scholar
(2)Bott, R.Non-degenerate critical manifolds. Annals of Math. 60 (1954), 248–261.CrossRefGoogle Scholar
(3)Freud, G. and Németh, G.On the Lp-norms of orthonormal Hermite functions. Stud. Sci. Math. Hung. 8 (1973), 399–404.Google Scholar
(4)Né, G.On the L 4-norm of orthonormal Laguerre polynomials. Stud. Sci. Math. Hung. 10 (1975), 243–246.Google Scholar
(5)Olver, F. W. J.Error bounds for the Liouville-Green (or WKB) approximation. Proc. Cambridge Philos. Soc. 57 (1961), 790–810.CrossRefGoogle Scholar
(6)Robin, L.Fonctions Sphériques de Legendre et Fonctions Sphériodales, T. II, Gauthier-Villars, Paris, 1958.Google Scholar
(7)Slater, L. J.Generalized Hypergeometric Functions (Cambridge University Press, 1966).Google Scholar
(8)Szegö, G.Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc, Providence, R.I., 1967.Google Scholar
(9)Titchmarsh, E. C.The Theory of Functions (Oxford University Press, London, Second Edition, 1939).Google Scholar
(10)Weinstein, A. Nonlinear stabilization of quasimodes, Proc. A.M.S. Symp. on Geometry of the Laplacian, Hawaii, 1979, Amer. Math. Soc. Colloq. Publ. 36 (1980), 301–318.Google Scholar