Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666295 | Advances in Mathematics | 2012 | 16 Pages |
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.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Dmitry Ryabogin,