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Positivity of the Jacobi–Cherednik intertwining operator and its dual
-
Léonard Gallardo
Published/Copyright:
March 19, 2010
Abstract
This paper is devoted to the study of the differential-difference Jacobi–Cherednik operator defined for f ∈ C1 (𝕣) by
T(k,k′)f(x) = f′(x) + (k coth(x) + k′ tanh(x))(f(x) – f(–x)) – (k + k′) f(–x),
where k > 0 and k′ ≥ 0 are two parameters, and to the positivity of the operator which intertwines T(k,k′) and the derivative operator 
.
Keywords.: Jacobi–Cherednik operator; intertwining operator; Laplace formula for the eigenfunctions; positivity of the intertwining kernel; intertwining dual operator
Received: 2009-02-04
Revised: 2009-04-08
Published Online: 2010-03-19
Published in Print: 2010-June
© de Gruyter 2010
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Articles in the same Issue
- An analog of Morgan's theorem for the Kontorovich–Lebedev transform
- Positivity of the Jacobi–Cherednik intertwining operator and its dual
- Absolute continuity of the representing measures of the Dunkl intertwining operator and of its dual and applications
- Cut-primitive directed graphs versus clan-primitive directed graphs
- On a class of variational-hemivariational inequalities involving set valued mappings
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