02680nam 2200565Ka 450 991048361810332120200520144314.03-642-25983-910.1007/978-3-642-25983-8(CKB)3360000000365821(SSID)ssj0000630009(PQKBManifestationID)11393320(PQKBTitleCode)TC0000630009(PQKBWorkID)10731542(PQKB)10389040(DE-He213)978-3-642-25983-8(MiAaPQ)EBC3070403(PPN)159086329(EXLCZ)99336000000036582120120228d2012 uy 0engurnn|008mamaatxtccrSpherical harmonics and approximations on the unit sphere an introduction /Kendall Atkinson, Weimin Han1st ed. 2012.Berlin ;New York Springerc20121 online resource (IX, 244 p. 19 illus., 11 illus. in color.) Lecture notes in mathematics,0075-8434 ;2044Bibliographic Level Mode of Issuance: Monograph3-642-25982-0 Includes bibliographical references and index.1 Preliminaries -- 2 Spherical Harmonics -- 3 Differentiation and Integration over the Sphere -- 4 Approximation Theory -- 5 Numerical Quadrature -- 6 Applications: Spectral Methods.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.Lecture notes in mathematics (Springer-Verlag) ;2044.Spherical harmonicsSpherical functionsSpherical harmonics.Spherical functions.515/.53Atkinson Kendall E54021Han Weimin287589MiAaPQMiAaPQMiAaPQBOOK9910483618103321Spherical harmonics and approximations on the unit sphere853807UNINA