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The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type A2
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Khalifa Trimèche
Published/Copyright:
April 1, 2015
Abstract
We consider the transmutation operators Vk and tVk associated with the Cherednik operators attached to the root system A2, called also in [Adv. Pure Appl. Math. 1 (2010), 293–323; Adv. Pure Appl. Math. 2 (2011), 223–246] the trigonometric Dunkl intertwining operator, and its dual. In this paper, we prove that the operators Vk and tVk are positivity preserving and allows positive integral representations. In particular, we deduce that the Opdam–Cherednik kernel is positive definite.
Keywords: Cherednik operators; root system of type A2; Transmutation operators; the trigonometric Dunkl intertwining operator and its dual
The author is grateful to the referee for his careful reading and useful comments.
Received: 2013-11-5
Accepted: 2014-11-7
Published Online: 2015-4-1
Published in Print: 2015-4-1
© 2015 by De Gruyter
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Keywords for this article
Cherednik operators;
root system of type A2;
Transmutation operators;
the trigonometric Dunkl intertwining operator and its dual
Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
- Some further estimates of the prolate spheroidal wave functions and their spectrum
- On the connectedness of the Chabauty space of a locally compact prosolvable group
- Holomorphically induced representations of exponential solvable semi-direct product groups ℝ ⋉ ℝn
- The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type A2
