TY - BOOK ID - 8359610 TI - Spherical harmonics and approximations on the unit sphere : an introduction AU - Atkinson, Kendall E. AU - Han, Weimin. PY - 2012 SN - 3642259820 3642259839 PB - Berlin ; New York : Springer, DB - UniCat KW - Engineering & Applied Sciences KW - Civil & Environmental Engineering KW - Operations Research KW - Applied Mathematics KW - Spherical harmonics. KW - Spherical functions. KW - Functions, Spherical KW - Functions, Potential KW - Potential functions KW - Mathematics. KW - Approximation theory. KW - Integral equations. KW - Partial differential equations. KW - Special functions. KW - Numerical analysis. KW - Physics. KW - Numerical Analysis. KW - Special Functions. KW - Approximations and Expansions. KW - Integral Equations. KW - Partial Differential Equations. KW - Physics, general. KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Mathematical analysis KW - Special functions KW - Partial differential equations KW - Equations, Integral KW - Functional equations KW - Functional analysis KW - Theory of approximation KW - Functions KW - Polynomials KW - Chebyshev systems KW - Math KW - Science KW - Spherical harmonics KW - Transcendental functions KW - Spheroidal functions KW - Harmonic analysis KW - Harmonic functions KW - Functions, special. KW - Differential equations, partial. UR - https://www.unicat.be/uniCat?func=search&query=sysid:8359610 AB - These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions. ER -