The Funk-Hecke formula, harmonic polynomials, and derivatives of radial distributions
Estrada, Ricardo
Boletim da Sociedade Paranaense de Matemática, Tome 37 (2017), / Harvested from Portal de Periódicos da UEM
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We give a version of the Funk-Hecke formula that holds with minimal assumptonsand apply it to obtain formulas for the distributional derivatives of radialdistributions in Rn of the typeYk􀀀rj(f (r)) ;where Yk is a harmonic homogeneous polynomial. We show that such derivatives havesimpler expressions than those of the form p􀀀r(f (r)) for a general polynomial p:

Publié le : 2017-01-01
DOI : https://doi.org/10.5269/bspm.v37i3.34198 
@article{34198,
     title = {The Funk-Hecke formula, harmonic polynomials, and derivatives of radial distributions},
     journal = {Boletim da Sociedade Paranaense de Matem\'atica},
     volume = {37},
     year = {2017},
     doi = {10.5269/bspm.v37i3.34198},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/34198}
}

Estrada, Ricardo. The Funk-Hecke formula, harmonic polynomials, and derivatives of radial distributions. Boletim da Sociedade Paranaense de Matemática, Tome 37 (2017) . doi : 10.5269/bspm.v37i3.34198. http://gdmltest.u-ga.fr/item/34198/