Reproducing kernel Hilbert spaces on manifolds: Sobolev and Diffusion spaces
Functional Analysis
2019-05-28 v1 Machine Learning
Machine Learning
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.
Keywords
Cite
@article{arxiv.1905.10913,
title = {Reproducing kernel Hilbert spaces on manifolds: Sobolev and Diffusion spaces},
author = {Ernesto De Vito and Nicole Mücke and Lorenzo Rosasco},
journal= {arXiv preprint arXiv:1905.10913},
year = {2019}
}