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Real Paley-Wiener theorems and Roe’s theorem associated with the Opdam-Cherednik transform. (English) Zbl 1408.46041

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.

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.)
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