# Greg Fasshauer

## Professor of Applied Mathematics

10 West 32nd Street, Chicago, IL 60616 (email)

Given a strictly positive definite 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 definite functions defined 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.