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Convex Bodies: The Brunn–Minkowski Theory, Second Edition by Rolf Schneider

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Appendix

Spherical harmonics

In several places in the geometry of convex bodies, spherical harmonics prove quite useful. In the present book, they are applied in Sections 3.3, 3.4, 3.5, 7.6 and 8.3, and some of the notes describe results that were obtained by means of this tool. In this appendix, we briefly collect, without proofs, the basic facts about spherical harmonics as they are needed in this book. For introductory material, including proofs, we refer to Müller [1454], Seeley [1764] and the literature quoted there; a more recent introduction is Atkinson and Han [98]. For the connections with representations of the rotation group we refer also to Coifman and Weiss [433]. For a more comprehensive view of the applications of Fourier series ...

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