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Reproducing Kernel Hilbert Spaces Associated with Analytic Translation-Invariant Mercer Kernels

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Abstract

In this article we study reproducing kernel Hilbert spaces (RKHS) associated with translation-invariant Mercer kernels. Applying a special derivative reproducing property, we show that when the kernel is real analytic, every function from the RKHS is real analytic. This is used to investigate subspaces of the RKHS generated by a set of fundamental functions. The analyticity of functions from the RKHS enables us to derive some estimates for the covering numbers which form an essential part for the analysis of some algorithms in learning theory.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, Beijing, 100875, China

    Hong-Wei Sun

  2. School of Science, Jinan University, Jinan, 250022, China

    Hong-Wei Sun

  3. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Ding-Xuan Zhou

Authors
  1. Hong-Wei Sun
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  2. Ding-Xuan Zhou
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Corresponding author

Correspondence to Hong-Wei Sun.

Additional information

The work is supported by City University of Hong Kong (Project No. 7001816), and National Science Fund for Distinguished Young Scholars of China (Project No. 10529101).

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Sun, HW., Zhou, DX. Reproducing Kernel Hilbert Spaces Associated with Analytic Translation-Invariant Mercer Kernels. J Fourier Anal Appl 14, 89–101 (2008). https://doi.org/10.1007/s00041-007-9003-z

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  • DOI: https://doi.org/10.1007/s00041-007-9003-z

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