Startseite The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman--Opdam theory on ℝd
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The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman--Opdam theory on ℝd

  • Khalifa Trimèche EMAIL logo
Veröffentlicht/Copyright: 12. Januar 2017
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Abstract

We consider the hypergeometric translation operators associated to the Cherednik operators and the Heckman–Opdam theory on d introduced by the author in [6]. Under some conditions on the root system and the multiplicity function, we prove in this paper that these operators are positivity preserving and allow positive integral representations. In particular, we deduce for the Opdam–Cherednik kernel and the Heckman–Opdam hypergeometric function the following main results:

  1. Their product formulas are positive integral transforms.

  2. We obtain for them best estimates.

MSC 2010: 33E30; 33C67; 51F15

Acknowledgements

The author is grateful to the referee for his excellent report and the interest he has shown in this paper.

References

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Received: 2014-4-10
Accepted: 2014-12-22
Published Online: 2017-1-12
Published in Print: 2017-4-1

© 2017 by De Gruyter

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