EAN: 9783642259821

SPHERICAL HARMONICS AND APPROXIMATIONS ON THE U...

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.

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