Abel means for orthogonal expansions of distributions on spheres, balls and simplices (Q497767)

The author shows that a point \(x\) is out of the support of a distribution \(T\) on the open unit simplex if and only if the orthogonal expansion of \(T\) is uniformly summable in Abel means to zero on a neighborhood of \(x\). For that he first proves a similar result about the Fourier-Laplace series of a distribution on the sphere in his paper [J. Korean Math. Soc. 41, No. 4, 755--772 (2004; Zbl 1066.46031)]. From this equivalence he derives one about orthogonal expansions on the ball, and finally the desired result on the simplex by applying the result of \textit{F. Dai} et al. [J. Funct. Anal. 265, No.~10, 2357--2387 (2013; Zbl 1283.42039)].