Author | Mรผller, Claus. author |
---|---|
Title | Analysis of Spherical Symmetries in Euclidean Spaces [electronic resource] / by Claus Mรผller |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0581-4 |
Descript | VIII, 226 p. online resource |
1 Notations and Basic Theorems> -- 1 The General Theory 9 -- ยง2 Primitive Spaces -- ยง3 The Completeness -- ยง4 The Funk-Hecke Formula -- ยง5 Representations and Interpolations -- ยง6 Homogeneous Harmonics -- 2 The Specific Theories -- ยง7 The Legendre Polynomials -- ยง8 The Laplace Integrals -- ยง9 The Gegenbauer Polynomials -- ยง10 The Associated Legendre Functions -- ยง1 The Associated Spaces yjn(q) -- ยง12 Harmonic Differential Operators -- ยง13 Maxwellโs Theory of Multipoles -- 3 Spherical Harmonics and Differential Equations -- ยง14 The Laplace-Beltrami Operators -- ยง15 Spherical Harmonics as Eigenfunctions -- ยง16 The Legendre Differential Equation -- ยง17 The Legendre Functions as Hypergeometric Functions -- 4 Analysis on the Complex Unit Spheres -- ยง18 Homogeneous Harmonics in ?q -- ยง19 Invariant Integrals on S*q-1 -- ยง20 Complexification of the Funk-Hecke Formula -- ยง21 An Alternative System of Legendre Functions -- 5 The Bessel Functions -- ยง22 Regular Bessel Functions -- ยง23 Regular Hankel Functions -- ยง24 Recursive and Asymptotic Relations -- ยง25 Addition Formulas for Hankel Functions of Order Zero -- ยง26 Exponential Integrals with Bessel Functions -- ยง27 The Traditional Notations -- 6 Integral Transforms -- ยง28 Fourier Integrals -- ยง29 The Fourier Representation Theorem -- ยง30 The Parseval Identity -- ยง31 Examples -- 7 The Radon Transform -- ยง32 Radon Transforms and Fourier Transforms -- ยง33 Radon Transforms and Spherical Symmetries -- ยง34 The Nicholson Formulas -- 8 Appendix -- ยง35 The ?-Function. -- ยง36 The Hypergeometric Function -- ยง37 Elementary Asymptotics -- References