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Variation Diminishing Convolution Kernels Associated with Dunkl operator
  • MONCEF DZIRI
MONCEF DZIRI
University of Tunis El Manar Faculty of Sciences of Tunis
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Abstract

Harmonic analysis associated with the Dunkl operator in one dimension was developed by many authors. Here we use these results to prove theorems analogous to those Schoenberg [9], and I.I. Hirschman [5] on variation diminishing convolution kernels. We give necessary and sufficient conditions such that an integrable function $\Phi$ is a variation diminishing convolution kernel.