# On Density in Radial Basis Approximation

Mon, 04/06/2012 - 14:00
Speaker:
Seminar:
Abstract:

We characterize the radial basis functions whose
scattered shifts form a fundamental system in
the space $L_{p}(\rrd)$. In particular, we show that for any even function $h$ from the space
$L_{2,{\rm loc}}(\rrd)$
the space formed by all possible linear combinations of
shifted radial basis functions $h(\|x+a\|)$, $a\in \rrd$, is dense in the
space $L_p(\rrd)$, $1\le p\le 2$, if
and only if the function $h$ is not a polynomial.