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 journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 89-101 |
| Journal / Publication | Journal of Fourier Analysis and Applications |
| Volume | 14 |
| Issue number | 1 |
| Publication status | Published - Feb 2008 |
Link(s)
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. © 2008 Birkhäuser Boston.
Research Area(s)
- Covering number, Derivative reproducing, Learning theory, Real analyticity, Reproducing kernel Hilbert space, Translation-invariant Mercer kernel
Citation Format(s)
Reproducing kernel hilbert spaces associated with analytic translation-invariant mercer kernels. / Sun, Hong-Wei; Zhou, Ding-Xuan.
In: Journal of Fourier Analysis and Applications, Vol. 14, No. 1, 02.2008, p. 89-101.
In: Journal of Fourier Analysis and Applications, Vol. 14, No. 1, 02.2008, p. 89-101.
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
