Emergent Mind
Reproducing kernel Hilbert spaces on manifolds: Sobolev and Diffusion spaces
(1905.10913)
Published May 27, 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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