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Multipliers of spherical harmonics and energy of measures on the sphere

Kathryn E. Hare Department of Pure Mathematics, University of Waterloo Maria Roginskaya Department of Mathematics, Chalmers Institute of Technology

TBD mathscidoc:1701.333005

Arkiv for Matematik, 41, (2), 281-294, 2002.2
We consider the operator,$f$(Δ) for Δ the Laplacian, on spaces of measures on the sphere in$R$^{$d$}, show how to determine a family of approximating kernels for this operator assuming that certain technical conditions are satisfied, and give estimates for the$L$^{2}-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$R$^{$d$}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.
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@inproceedings{kathryn2002multipliers,
  title={Multipliers of spherical harmonics and energy of measures on the sphere},
  author={Kathryn E. Hare, and Maria Roginskaya},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203607447689814},
  booktitle={Arkiv for Matematik},
  volume={41},
  number={2},
  pages={281-294},
  year={2002},
}
Kathryn E. Hare, and Maria Roginskaya. Multipliers of spherical harmonics and energy of measures on the sphere. 2002. Vol. 41. In Arkiv for Matematik. pp.281-294. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203607447689814.
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