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

• URL: http://arxiv.org/abs/2002.03171v2
• Date: Fri, 13 Mar 2020 14:28:39 GMT
• Title: Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Space
• Authors: Ingo Steinwart
• Abstract summary: 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.
• Score: 2.7793394375935088
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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