This is a preview of subscription content, log in via an institution to check access.
References
Askey, R. andFitch, J., Integral representations for Jacobi polynomials and some applications.J. Math. Anal. Appl.,26 (1969), 411–437.
Braaksma, B. L. J., andMeulenbeld, B., Integral transforms with generalized Legendre functions as kernels.Compositio Math.,18 (1967), 235–287.
Chébli, H., Sur la positivité des opératerurs de “translation généralisée” associés à un opérateur de Sturm-Liouville sur [0, ∞[.C. R. Acad. Sci. Paris, A,275 (1972), 601–604.
Chébli, H., Positivité des opérateurs de translation généralisée associés à un opérateur de Sturm-Liouville sur ]0, ∞[.Séminaire de Théorie Spectrale, année 1972–73 Institut de Recherche Mathématique Avancée, Strasbourg.
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.
Dunford, N. andSchwartz, J. T.,Linear Operators, Vol. II. Interscience Publishers, New York, 1963.
Erdélyi, A., Magnus, W., Oberhettinger, F. andTricomi, F. G.,Higher Transcendental Functions, Vol. I. McGraw-Hill, New York, 1953.
Erdélyi, A., Magnus, W., Oberhettiger, F. andTricomi, F. G.,Tables of integral transforms, Vol. II. McGraw-Hill, New York, 1954.
Flensted-Jensen, M., Paley-Wiener type theorems for a differential operator connected with symmetric spaces.Ark. Mat.,10, (1972), 143–162.
Flensted-Jensen, M., Spherical functions on rank one symmetric spaces and generalizations.Proceedings Symposia Pure Mathematics, Vol. 26, American Mathematical Society, Providence (R. I.), 1973.
Flensted-Jensen, M., The spehrical functions on the universal covering ofSU(n−1,1)/SU(n−1).Københavns Universitet Mat. Institut Preprint Series, (1973), No. 1.
Flensted-Jensen, M. andKoornwinder, T. H., The convolution structure for Jacobi function expansions.Ark. Mat.,11 (1973), 245–262.
Flensted-Jensen, M. andRagozin, D. L., Spherical functions are Fourier transforms ofL 1-functions.Ann. Sci. Ecole Norm. Sup. (4),6 (1973), 457–458.
Gasper, G., Formulas of the Dirichlet-Mehler type.Prepublication (1973).
Helgason, S., An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces.Math. Ann.,165, (1966), 297–308.
Helgason, S., A duality for symmetric spaces with applications to group representations.Advances in Math.,5 (1970), 1–154.
Hörmander, L.,Linear partial differential operators. Springer-Verlag, Berlin, 1963.
Koornwinder, T. H., The addition formula for Jacobi polynomials, I. Summary of results.Nederl. Akad. Wetensch. Proc. A,75=Indag. Math.,34 (1972), 188–191.
Koornwinder, T. H., Jacobi polynomials, II. An analytic proof of the product formula.SIAM J. Math. Anal.,5 (1974), 125–137.
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.
Olevskiį, M. N., On the representation of an arbitrary function in the form of an integral with a kernel containing a hypergeometric function.Dokl. Akad. Nauk. SSSR.,69 (1949), 11–14 (Russian).
Titchmarsh, E. C.,The theory of functions. Oxford University Press second edition, 1939.
Titchmarsh, E. C. Eigenfunction expansions associated with second-order differential equations, Vol. I. Oxford University Press, 1946.
Braaksma, B. L. J. andDe Snoo, H. S. V., Generalized translation operators associated with a singular differential operator. “Proceedings of a Conference on the Theory of Ordinary and Partial Differential Equations held in Dundee, Scotland, March 1974”, Lecture Notes in Math., Springer-Verlag. (To appear.)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koornwinder, T. A new proof of a Paley—Wiener type theorem for the Jacobi transform. Ark. Mat. 13, 145–159 (1975). https://doi.org/10.1007/BF02386203
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02386203