100 Years of Fourier Series and Spherical Harmonics in Convexity

Abstract

Various examples are given that illustrate the fact that Fourier series and spherical harmonics are sometimes essential tools for proving interesting theorems in the geometry of convex sets. To make the article more self-contained most pertinent definitions are stated and the underlying geometric and analytic facts are briefly discussed.KeywordsFourier SeriesConvex BodySpherical HarmonicSupport FunctionLegendre PolynomialThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.