SPHERICAL HARMONICS ASSOCIATED TO THE LAPLACE-BESSEL OPERATOR AND GENERALIZED SPHERICAL CONVOLUTIONS
ANALYSIS AND APPLICATIONS, vol.1, no.1, pp.81-109, 2003 (SCI-Expanded)
- Publication Type: Article / Article
- Volume: 1 Issue: 1
- Publication Date: 2003
- Doi Number: 10.1142/s0219530503000077
- Journal Name: ANALYSIS AND APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.81-109
- Keywords: Spherical harmonics, Fourier-Bessel transform, spherical convolutions
- Akdeniz University Affiliated: Yes
Abstract
A theory of spherical harmonics associated to the Laplace-Bessel differential operator is developed. Natural analogs of the Plancherel theory, the Laplace formula, the Funk-Hecke formula, the product formula, and the addition theorem are obtained. Symmetry properties of the Fourier-Bessel transform, decompositions of smooth functions, and convolution operators are studied.