Fundamental sets of functions on spheres
نویسنده
چکیده
Let S be the unit sphere in R and let 〈 · , · 〉 denote the usual inner product in R. We characterize those functions K in L([−1, 1]), p ≥ 1, for which the associated set of zonal functions {x ∈ S → K(〈x, y〉) : y ∈ S } is fundamental in L(S). We then study fundamentality of sets generated by either spherical convolution or spherical shifting, thus providing methods of construction of fundamental sets in L(S).
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