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October 2003 Multipliers of spherical harmonics and energy of measures on the sphere
Kathryn E. Hare, Maria Roginskaya
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Ark. Mat. 41(2): 281-294 (October 2003). DOI: 10.1007/BF02390816

Abstract

We consider the operator, f(Δ) for Δ the Laplacian, on spaces of measures on the sphere in Rd, show how to determine a family of approximating kernels for this operator assuming that certain technical conditions are satisfied, and give estimates for the L2-norm of f(Δ)μ in terms of the energy of the measure μ. We derive a formula, analogous to the classical formula relating the energy of a measure on Rd with its Fourier transform, comparing the energy of a measure on the sphere with the size of its spherical harmonics. An application is given to pluriharmonic measures.

Funding Statement

This research was done while the first author enjoyed the hospitality of the Department of Mathematics of Göteborg University and Chalmers Institute of Technology. It was supported in part by NSERC and the Swedish natural sciences research council.

Citation

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Kathryn E. Hare. Maria Roginskaya. "Multipliers of spherical harmonics and energy of measures on the sphere." Ark. Mat. 41 (2) 281 - 294, October 2003. https://doi.org/10.1007/BF02390816

Information

Received: 18 February 2002; Published: October 2003
First available in Project Euclid: 31 January 2017

zbMATH: 1034.43007
MathSciNet: MR2011922
Digital Object Identifier: 10.1007/BF02390816

Rights: 2003 © Institut Mittag-Leffler

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Vol.41 • No. 2 • October 2003
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