POSITIVITY OF THE TRANSMUTATION OPERATORS
AND ABSOLUTE CONTINUITY OF THEIR
REPRESENTING MEASURES FOR
A ROOT SYSTEM ON Rd
AND ABSOLUTE CONTINUITY OF THEIR
REPRESENTING MEASURES FOR
A ROOT SYSTEM ON Rd
Abstract. We consider the transmutation operators 
and
associated respectively with the Cherednik
operators and the Heckman-Opdam theory, called also in [9], [10] the
trigonometric Dunkl intertwining operators and their dual paper. In
this paper we prove that the operators and
are positivity preserving and allows positive integral
representations. Next we study the absolute continuity of their
representing measures and we deduce that the Opdam-Cherednik kernel
and the Heckman-Opdam hypergeometric function are positive definite.
and
associated respectively with the Cherednik
operators and the Heckman-Opdam theory, called also in [9], [10] the
trigonometric Dunkl intertwining operators and their dual paper. In
this paper we prove that the operators and
are positivity preserving and allows positive integral
representations. Next we study the absolute continuity of their
representing measures and we deduce that the Opdam-Cherednik kernel
and the Heckman-Opdam hypergeometric function are positive definite.
AMS Subject classification: 33E30,33C67, 47B34, 51F15
Keywords and phrases: Cherednik operators, Heckman-Opdam theory, root system on Rd, transmutation operators, trigonometric Dunkl intertwining operators, absolute continuity of the representing measures
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DOI: 10.12732/ijam.v28i4.10
Volume: 28
Issue: 4
Year: 2015
