Titlebook: Spherical Harmonics and Approximations on the Unit Sphere: An Introduction; Kendall Atkinson,Weimin Han Book 2012 Springer-Verlag Berlin H

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Preliminaries,The study of spherical harmonics has a long history, over 200 years by now. Classical spherical harmonics on the unit sphere of three dimensional Euclidean space can be viewed as extensions of trigonometric functions on the unit circle.

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Spherical Harmonics,This chapter presents a theory of spherical harmonics from the viewpoint of invariant linear function spaces on the sphere. It is shown that the system of spherical harmonics is the only system of invariant function spaces that is both complete and closed, and cannot be reduced further.

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Differentiation and Integration over the Sphere,In this chapter, we discuss some properties and formulas for differentiation and integration involving spherical harmonics.

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Approximation Theory,For functions of a single variable, there is a rich literature on best approximations by ordinary polynomials and by trigonometric polynomials.

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Applications: Spectral Methods,This chapter begins with two illustrations of the application of the material from the preceding chapters.

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Kendall Atkinson,Weimin Hans in this study is outlined in Table 1. The questionnaire was divided up into four parts; in the first part, the indications were specifled. The number of procedures carried out for each indication was requested. The success rate was then established, the total number of complications observed, and

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