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A new proof of a Paley-Wiener type theorem for the Jacobi transform. (English) Zbl 0303.42022

42A38Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
44A15Special transforms (Legendre, Hilbert, etc.)
26A33Fractional derivatives and integrals (real functions)
33C05Classical hypergeometric functions, ${}_2F_1$
Full Text: DOI
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[5] Chébli, H., Sur un théorème de Paley-Wiener associé à la decomposition spectrale d’un opérateur de Sturm-Liouville sur ]0, .J. Functional Anal.,17 (1974), 447--461. · Zbl 0288.47040 · doi:10.1016/0022-1236(74)90052-4
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[13] Flensted-Jensen, M. andRagozin, D. L., Spherical functions are Fourier transforms ofL 1-functions.Ann. Sci. Ecole Norm. Sup. (4),6 (1973), 457--458. · Zbl 0293.22020
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[19] Koornwinder, T. H., Jacobi polynomials, II. An analytic proof of the product formula.SIAM J. Math. Anal.,5 (1974), 125--137. · Zbl 0269.33015 · doi:10.1137/0505014
[20] Mehler, F. G., Ueber eine mit den Kugel und Cylinderfunctionen verwnadte Function und ihre. Anwendung in der Theorie der Elektricitätsvertheilung.Math. Ann.,18 (1881), 161--194. · Zbl 13.0779.02 · doi:10.1007/BF01445847
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