Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Space
Not on the map. Why?
Abstract (arXiv)
Given an uncountable, compact metric space, we show that there exists no reproducing kernel Hilbert space that contains the space of all continuous functions on this compact space.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Feb 2020.
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Citing papers per year: 2021: 1; 2022: 0; 2023: 0; 2024: 2; 2025: 2; 2026: 1.
6 papers.
- 2024Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networkscited by 8
- 2021Topology, Convergence, and Reconstruction of Predictive Statescited by 5
- 2025Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operatorscited by 2
- 2026Shallow ReLUs Networks in Lp-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalizationcited by 2
- 2024Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spacescited by 0
- 2025On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spacescited by 0
- 2026Shallow ReLUs Networks in Lp-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization18 May 2026
- 2025Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators30 Sep 2025
- 2025On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces18 Apr 2025
- 2024Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces9 Aug 2024
- 2024Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks29 Apr 2024
- 2021Topology, Convergence, and Reconstruction of Predictive States19 Sep 2021