Abstract
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 typeYkrj(f (r)) ;where Yk is a harmonic homogeneous polynomial. We show that such derivatives havesimpler expressions than those of the form pr(f (r)) for a general polynomial p:
Publisher
Sociedade Paranaense de Matematica
Reference26 articles.
1. Three-dimensional Fourier transforms, integrals of spherical Bessel functions, and novel delta function identities;Adkins;Bull Allahabad Math Soc,2016
2. 2. Axler, S., Bourdon, P., and Ramey, W., Harmonic Function Theory, second edition, Springer, New York, 2001.
3. 3. Bateman Manuscript Project Staff, Higher transcendental functions, vol 2, McGraw Hill, New York, 1953.
4. 4. Erdelyi, A., Die Funksche Integralgleichung der Kugelflachenfunktionen und ihre Ubertragung auf die Uberkugel, Math. Ann. 115 (1938), 456-465.
5. 5. Estrada, R., On radial functions and distributions and their Fourier transforms, J. Fourier Anal. Appls. 20 (2013), 301-320.
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