Reproducing kernel Hilbert spaces on manifolds: Sobolev and Diffusion spaces
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Abstract (arXiv)
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.
Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 May 2019.
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Citing papers per year: 2021: 1; 2022: 3; 2023: 4; 2024: 3; 2025: 2; 2026: 1.
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- 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact casecited by 25
- 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
- 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spacescited by 15
- 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
- 2023Intrinsic Gaussian Vector Fields on Manifoldscited by 8
- 2023Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifoldscited by 6
- 2022On the speed of uniform convergence in Mercer's theoremcited by 5
- 2023Implicit Manifold Gaussian Process Regressioncited by 4
- 2024Residual Deep Gaussian Processes on Manifoldscited by 2
- 2025Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processescited by 2
- 2025Expressive Power of Deep Networks on Manifolds: Simultaneous Approximationcited by 2
- 2024Spectral Algorithms on Manifolds through Diffusioncited by 1
- 2026Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems5 May 2026
- 2025Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation11 Sep 2025
- 2025Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processes24 Mar 2025
- 2024Residual Deep Gaussian Processes on Manifolds31 Oct 2024
- 2024Diffusion-based Semi-supervised Spectral Algorithm for Regression on Manifolds18 Oct 2024
- 2024Spectral Algorithms on Manifolds through Diffusion6 Mar 2024
- 2023Implicit Manifold Gaussian Process Regression30 Oct 2023
- 2023Intrinsic Gaussian Vector Fields on Manifolds28 Oct 2023
- 2023Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifolds19 Sep 2023
- 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces30 Jan 2023
- 2022Spectral Representation Learning for Conditional Moment Models29 Oct 2022
- 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case31 Aug 2022
2 more
- 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact casecited by 25
- 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
- 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spacescited by 15
- 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
- 2023Intrinsic Gaussian Vector Fields on Manifoldscited by 8
- 2023Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifoldscited by 6
- 2022On the speed of uniform convergence in Mercer's theoremcited by 5
- 2023Implicit Manifold Gaussian Process Regressioncited by 4
- 2024Residual Deep Gaussian Processes on Manifoldscited by 2
- 2025Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processescited by 2
- 2025Expressive Power of Deep Networks on Manifolds: Simultaneous Approximationcited by 2
- 2024Spectral Algorithms on Manifolds through Diffusioncited by 1
12 most cited of 14 All 14 (JSON)
- 2026Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems5 May 2026
- 2025Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation11 Sep 2025
- 2025Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processes24 Mar 2025
- 2024Residual Deep Gaussian Processes on Manifolds31 Oct 2024
- 2024Diffusion-based Semi-supervised Spectral Algorithm for Regression on Manifolds18 Oct 2024
- 2024Spectral Algorithms on Manifolds through Diffusion6 Mar 2024
- 2023Implicit Manifold Gaussian Process Regression30 Oct 2023
- 2023Intrinsic Gaussian Vector Fields on Manifolds28 Oct 2023
- 2023Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifolds19 Sep 2023
- 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces30 Jan 2023
- 2022Spectral Representation Learning for Conditional Moment Models29 Oct 2022
- 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case31 Aug 2022
12 newest of 14 All 14 (JSON)