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We consider the harmonic analysis associated with the Dunkl operators on Rd. We study the Dunkl mean-periodic functions on the space e(Rd) (the space of C∞-functions). We characterize also the continuous linear mappings from e(Rd) into itself which commute with the Dunkl operators.

The Commutants of the Dunkl Operators on &lt;i&gt; ε&lt;/i&gt;(R&lt;sup&gt;d&lt;/sup&gt;)

The Commutants of the Dunkl Operators on <i> ε</i>(R<sup>d</sup>)