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A note on the uncertainty principle for the Dunkl transform. (English) Zbl 0976.33015

The author gives two versions of the uncertainty principle for the Dunkl transform. The first one is a Heisenberg-type inequality of the form \(\|x f\|\|\xi\widehat f\|\geq C\|f\|^2\) in natural \(L^2\)-norms, the second one a Hardy-type theorem giving a restriction on the simultaneous decay at infinity of \(f\) and \(\widehat f\). The author points out that the first of these facts has previously been proved by M. Rösler [Bull. Aust. Math. Soc. 59, No. 3, 353-360 (1999; Zbl 0939.33012)].

MSC:

33C80 Connections of hypergeometric functions with groups and algebras, and related topics

Citations:

Zbl 0939.33012
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