Andersen, Nils Byrial Real Paley-Wiener theorems and Roe’s theorem associated with the Opdam-Cherednik transform. (English) Zbl 1408.46041 J. Math. Anal. Appl. 427, No. 1, 47-59 (2015). Summary: We reconsider Roe’s theorem associated with Jacobi-Cherednik operators. We first prove two new real Paley-Wiener theorems for the Opdam-Cherednik transform, characterizing those functions whose transform has support inside or outside intervals. As a corollary, we get a characterization of those functions whose transform has support at the endpoints, which we use to prove our version of Roe’s theorem. Cited in 1 ReviewCited in 6 Documents MSC: 46F12 Integral transforms in distribution spaces 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:Opdam-Cherednik transform; real Paley-Wiener theorem; Roe’s theorem PDFBibTeX XMLCite \textit{N. B. Andersen}, J. Math. Anal. Appl. 427, No. 1, 47--59 (2015; Zbl 1408.46041) Full Text: DOI