L p Error Estimates for Scattered Data Interpolation On Spheres

In this article, working with the sphere 𝕊 d embedded in the (d + 1)-dimensional Euclidean space ℝ d+1 as the underlying manifold, we obtain an error estimate for interpolating functions f ∈ H μ from shifts of a smooth positive definite function defined on 𝕊 d , where H μ is a Sobolev space. We also get an L p error estimate for f by using a method of Duchon framework.

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