Abstract
From the Dunkl analogue of Gegenbauer’s expansion of the plane wave, we derive an explicit closed formula for the spectrum of a right inverse of the Dunkl operator. This is done by stating the problem in such a way it is possible to use the technique due to Ismail and Zhang.
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Research of the first author supported by FCT project SPTDC/MAT/114394/2009, POCI 2010 and FSE, and Austrian Science Fund (FWF) START-project FLAME (“Frames and Linear Operators for Acoustical Modeling and Parameter Estimation”, Y 551-N13). Research of the second and third authors supported by grant MTM2012-36732-C03-02 of the DGI.
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Abreu, L.D., Ciaurri, Ó. & Varona, J.L. The spectrum of the right inverse of the Dunkl operator. Rev Mat Complut 26, 471–483 (2013). https://doi.org/10.1007/s13163-012-0110-2
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DOI: https://doi.org/10.1007/s13163-012-0110-2