The Funk-Hecke formula, harmonic polynomials, and derivatives of radial distributions
We give a version of the Funk-Hecke formula that holds with minimal assumptons and apply it to obtain formulas for the distributional derivatives of radial distributions in Rn of the type Yk r j (f (r)) ; where Yk is a harmonic homogeneous polynomial. We show that such derivatives have simpler e...
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| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2019-07-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/34198 |
| Summary: | We give a version of the Funk-Hecke formula that holds with minimal assumptons
and apply it to obtain formulas for the distributional derivatives of radial
distributions in Rn of the type
Yk
r
j
(f (r)) ;
where Yk is a harmonic homogeneous polynomial. We show that such derivatives have
simpler expressions than those of the form p
r
(f (r)) for a general polynomial p: |
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| ISSN: | 0037-8712 2175-1188 |