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Reproducing kernel Hilbert spaces on manifolds: Sobolev and Diffusion spaces (1905.10913v1)
Published 27 May 2019 in math.FA, cs.LG, and stat.ML
Abstract: We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of smoother RKHS that we call diffusion spaces. We illustrate the general results with a number of detailed examples.
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