Reproducing kernel hilbert spaces associated with analytic translation-invariant mercer kernels

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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  • Hong-Wei Sun
  • Ding-Xuan Zhou

Related Research Unit(s)


Original languageEnglish
Pages (from-to)89-101
Journal / PublicationJournal of Fourier Analysis and Applications
Issue number1
Publication statusPublished - Feb 2008


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. © 2008 Birkhäuser Boston.

Research Area(s)

  • Covering number, Derivative reproducing, Learning theory, Real analyticity, Reproducing kernel Hilbert space, Translation-invariant Mercer kernel