References
Bhanu Murthy, T. S.: Plancherel's measure for the factor spaceSL(n, R)/SO(n, R). Doklady Akad. Nauk SSSR133, 503–506 (1960).
—— The assymptotic behavior of zonal spherical functions on the Siegel upper half-plane. Doklady Akad. Nauk SSSR135, 1027–1029 (1960).
Ehrenpreis, L., andF. I. Mautner: Some properties of the Fourier transform on semi-simple Lie groups, I. Ann. Math.61, 406–439 (1955); II. Trans. Am. Math. Soc.84, 1–55 (1957).
Gindikin, S. G., andF. I. Karpelevič: Plancherel measure of Riemannian symmetric spaces of nonpositive curvature. Doklady Akad. Nauk SSSR145, 252–255 (1962).
Harish-Chandra: Spherical functions on a semisimple Lie group, I, II. Am. J. Math.80, 241–310, 553–613 (1958).
—— Some results on differential equations and their applications. Proc. Nat. Acad. Sci. USA45, 1763–1764 (1959).
Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962.
—— Duality and Radon transform for symmetric spaces. Am. J. Math.85, 667–692 (1963).
—— Fundamental solutions of invariant differential operators on symmetric spaces. Am. J. Math.86, 565–601 (1964).
Hörmander, L.: Linear partial differential operators. Berlin-Göttingen-Heidelberg: Springer 1963.
Magnus, W., u.R. Oberhettinger: Formeln und Sätze für die speziellen Funktionen der mathematischen Physik. Berlin-Göttingen-Heidelberg: Springer 1948.
Paley, R., andN. Wiener: Fourier transforms in the complex domain. Am. Math. Soc. Colloquium, New York, 1934.
Schwartz, L.: Théorie des Distributions, I, II. Paris: Hermann 1950, 1951.
Takahashi, R.: Sur les répresentations unitaires des groupes de Lorentz généralisés. Bull. Soc. Math. France91, 289–433 (1963).
Titchmarsh, E. C.: The theory of functions. 2nd edition. Oxford University Press 1939.
Author information
Authors and Affiliations
Additional information
Work supported in part by the National Science Foundation, NSF GP-2600.
Rights and permissions
About this article
Cite this article
Helgason, S. An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces. Math. Ann. 165, 297–308 (1966). https://doi.org/10.1007/BF01344014
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01344014