# On Density in Radial Basis Approximation

Seminar
Speaker
Prof. Vitaly E. Maiorov, Technion
Date
04/06/2012 - 14:00Add to Calendar 2012-06-04 14:00:00 2012-06-04 14:00:00 On Density in Radial Basis Approximation 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. אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
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.

תאריך עדכון אחרון : 21/05/2012