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- W2016186043 abstract "The Dunkl operators involve a multiplicity function k as parameter [C.F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989) 167–183]. For positive real values of this function, we consider on the Schwartz space S(RN) a representation ωk of sl(2,R) defined in terms of the Dunkl–Laplacian operator. By means of a beautiful theorem due to E. Nelson, we prove that ωk exponentiates to a unique unitary representation of the universal covering group of SL(2,R). The representation theory is used to derive an identity of Bochner type for the Dunkl transform." @default.
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- W2016186043 date "2007-09-01" @default.
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- W2016186043 title "On the integrability of a representation of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi mathvariant=fraktur>sl</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant=double-struck>R</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>" @default.
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- W2016186043 doi "https://doi.org/10.1016/j.jfa.2007.04.022" @default.
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