Absolute continuity of the measures of the Dunkl intetwining operator and its dualand applications

dc.creatorKhalifa, Trimeche
dc.date2007-06-11
dc.date.accessioned2026-07-07T08:04:52Z
dc.date.available2026-07-07T08:04:52Z
dc.descriptionIn this paper we consider the representing measures $μ_{x},x\in \QTR{Bbb}{R}^{d}$, and $ν_{y},y\in \QTR{Bbb}{R}^{d}$, of the Dunkl intertwining operator and of its dual. When the multiplicity function is positive, we prove that for all $x\in \QTR{Bbb}{R}_{\QTO{mbox}{reg}}^{d}$ we have $dμ_{x}(y)=\QTR{cal}{K}(x,y)dy$ and for almost all $y\in \QTR{Bbb}{R}^{d}$ we have $dν_{y}(x)=\QTR{cal}{K}(x,y)ω_{k}(x)dx,$ where $\QTR{cal}{K}(x,.)$ is a positive integrable function on $\QTR{Bbb}{R}^{d}$ with support in $\{y\in \QTR{Bbb}{R}^{d}/\Vert y\Vert \leq \Vert x\Vert \}$ and the function $\QTR{cal}{K}(.,y)$ is locally integrable on $\QTR{Bbb}{R}^{d}$ with respect to the measure $ω_{k}(x)dx$ and with support in $\{x\in \QTR{Bbb}{R}^{d}/\Vert x\Vert \geq \Vert y\Vert \}$. Next we present some applications of this result.
dc.identifierhttps://arxiv.org/abs/0706.1407
dc.identifierhttp://arxiv.org/abs/0706.1407
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130124
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subject33C80, 51F15, 44A15
dc.titleAbsolute continuity of the measures of the Dunkl intetwining operator and its dualand applications
dc.typetext

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