Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Space

2020/02/08 by Ingo Steinwart, Steinwart, Ingo
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2002.03171

openalex publication_date 2020/02/08 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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.

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