Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics, 2044) 2012th Edition by Kendall Atkinson (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review From the reviews:“The book concentrates on the theory of spherical harmonics on the unit sphere of a general d-dimensional Euclidian space. It summarizes the results related to Legendre and Gegenbauer polynomials as well as the theory of differentiation and integration over the d-dimensional unit sphere and the associated function spaces. … The style of material presentation … make the theory described in the book accessible to a wider audience of readers with only some basic knowledge in the functional analysis and measure theory.” (Vladimir L. Makarov, Zentralblatt MATH, Vol. 1254, 2013)“This is a very well-written, self-contained monograph on spherical harmonics. It is an excellent reference source for researchers and graduate students who are interested in polynomial approximation, numerical integration, differentiation and solution of partial differential and integral equations over the sphere.” (Feng Dai, Mathematical Reviews, January, 2013) From the Back Cover These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well asan 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Book’s contents are great! A more modern approach. The Book’s qualities despite the fact of being a “print on demand” version of the book, they are over average. Laser print was used and it has some color images. There are no missing characters so I would say this is a very decent copy.

⭐

Keywords

Free Download Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics, 2044) 2012th Edition in PDF format
Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics, 2044) 2012th Edition PDF Free Download
Download Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics, 2044) 2012th Edition 2012 PDF Free
Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics, 2044) 2012th Edition 2012 PDF Free Download
Download Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics, 2044) 2012th Edition PDF
Free Download Ebook Spherical Harmonics and Approximations on the Unit Sphere: An Introduction (Lecture Notes in Mathematics, 2044) 2012th Edition