## Generalized native spaces

Erickson, JF, Fasshauer GENeamtu, M, Schumaker LL.  2008.

### Book Title:

Approximation Theory XII: San Antonio 2007

133–142

Nashboro Press

### Abstract:

Given a strictly positive de finite function, we generalize the usual reproducing kernel Hilbert space type of native space construction in order to create {\$Lˆp\$} based types of native spaces for \$1 {\textless} p {\textbackslash}le 2\$. These spaces are Banach spaces, but when \$p = 2\$ we recover the usual native space. While giving up on the Hilbert part of the {RKHS} framework we are still able to recover function values with the help of Fourier transforms since we are using strictly positive de finite functions defi ned on all of {\${\textbackslash}mathbb{R}ˆd\$.} We obtain generalized generic power function error estimates.

Citation:
Erickson, JF, Fasshauer GE.  2008.  Generalized native spaces. Approximation Theory XII: San Antonio 2007. :133–142.