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Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions. (English) Zbl 1348.41010

Summary: The purpose of this paper is to get error estimates for spherical basis function (SBF) interpolation and approximation for target functions in Sobolev spaces less smooth than the SBFs, and to show that the rates achieved are, in a sense, best possible. In addition, we establish a Bernstein-type theorem, where the smallest separation between data sites plays the role of a Nyquist frequency. We then use these Bernstein-type estimates to derive inverse estimates for interpolation via SBFs.

MSC:

41A25 Rate of convergence, degree of approximation
41A05 Interpolation in approximation theory
41A63 Multidimensional problems
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