SPHERICAL HARMONICS ASSOCIATED TO THE LAPLACE-BESSEL OPERATOR AND GENERALIZED SPHERICAL CONVOLUTIONS
ANALYSIS AND APPLICATIONS, cilt.1, sa.1, ss.81-109, 2003 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 1 Sayı: 1
- Basım Tarihi: 2003
- Doi Numarası: 10.1142/s0219530503000077
- Dergi Adı: ANALYSIS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Sayfa Sayıları: ss.81-109
- Anahtar Kelimeler: Spherical harmonics, Fourier-Bessel transform, spherical convolutions
- Akdeniz Üniversitesi Adresli: Evet
Özet
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.