Article ID Journal Published Year Pages File Type
4666295 Advances in Mathematics 2012 16 Pages PDF
Abstract

Let ff and gg be two continuous functions on the unit sphere Sn−1Sn−1 in RnRn, n≥3n≥3, and let their restrictions to any one-dimensional great circle EE coincide after some rotation ϕEϕE of this circle: f(ϕE(θ))=g(θ)∀θ∈Ef(ϕE(θ))=g(θ)∀θ∈E. We prove that in this case f(θ)=g(θ)f(θ)=g(θ) or f(θ)=g(−θ)f(θ)=g(−θ) for all θ∈Sn−1θ∈Sn−1. This answers the question posed by Richard Gardner and Vladimir Golubyatnikov.

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Physical Sciences and Engineering Mathematics Mathematics (General)
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