On non-inclusion of certain functions in reproducing kernel Hilbert\n spaces

2021/02/21 by Toni Karvonen, Karvonen, Toni
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2102.10628

openalex publication_date 2021/02/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We use a classical characterisation to prove that functions which are bounded\naway from zero cannot be elements of reproducing kernel Hilbert spaces whose\nreproducing kernels decays to zero in a suitable way. The result is used to\nstudy Hilbert spaces on subsets of the real line induced by analytic\ntranslation-invariant kernels which decay to zero at infinity.\n

Related

• Remark on the theory of reproducing kernels
• Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Space
• Which Spaces can be Embedded in Reproducing Kernel Hilbert Spaces?
• Four Properties of Reproducing Kernel Hilbert Spaces
• Reproducing kernel Hilbert spaces and Mercer theorem