@incollection{AST_1985__S131__151_0, author = {Helgason, Sigurdur}, title = {The {Fourier} transform on symmetric spaces}, booktitle = {\'Elie Cartan et les math\'ematiques d'aujourd'hui - Lyon, 25-29 juin 1984}, series = {Ast\'erisque}, pages = {151--164}, publisher = {Soci\'et\'e math\'ematique de France}, number = {S131}, year = {1985}, mrnumber = {837200}, zbl = {0611.43005}, language = {en}, url = {http://www.numdam.org/item/AST_1985__S131__151_0/} }
TY - CHAP AU - Helgason, Sigurdur TI - The Fourier transform on symmetric spaces BT - Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984 AU - Collectif T3 - Astérisque PY - 1985 SP - 151 EP - 164 IS - S131 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_1985__S131__151_0/ LA - en ID - AST_1985__S131__151_0 ER -
%0 Book Section %A Helgason, Sigurdur %T The Fourier transform on symmetric spaces %B Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984 %A Collectif %S Astérisque %D 1985 %P 151-164 %N S131 %I Société mathématique de France %U http://www.numdam.org/item/AST_1985__S131__151_0/ %G en %F AST_1985__S131__151_0
Helgason, Sigurdur. The Fourier transform on symmetric spaces, dans Élie Cartan et les mathématiques d'aujourd'hui - Lyon, 25-29 juin 1984, Astérisque, no. S131 (1985), pp. 151-164. http://www.numdam.org/item/AST_1985__S131__151_0/
[1] Les espaces symétriques non compacts, C.R. Acad. Sci., t. 240, 1955, p. 2370-2372 | MR | Zbl
. -Les espaces symétriques non compacts, C.R. Acad. Sci., t. 241, 1955, p. 1696-1698. | MR | Zbl
. -[2] Les espaces symétriques non compacts, Ann. École Norm. Sup., t. 74, 1957, p. 85-177. | DOI | EuDML | Numdam | MR | Zbl
. -[3] Plancherel's measure for the factor space , Dokl. Akad. Nauk, SSSR, t. 133, 1960, p. 503-506. | MR | Zbl
. -[4] Sur la détermination d'un système orthogonal complet dans un espace de Riemann symétrique clos, Rend. Circ.Mat. Palermo, t. 53, 1929, p. 217-252. | DOI | JFM
. -[5] Notice sur les travaux scientifiques. Oeuvres Complètes, Part I, Vol. I. - Paris, Gauthier-Villars, 1952. | Zbl
. -[6] Une formule de type Mehler-Heine pour les zonales d'un espace riemannien symétrique, Studia Math., t. 57, 1976, p. 27-32. | DOI | EuDML | MR | Zbl
. -[7] Asymptotic expansions of Eisenstein integrals and Fourier transform on symmetric spaces, J. Funct. Anal., t. 34, 1979, p. 167-216. | DOI | MR | Zbl
. -[8] The Fourier transform of the Schwartz space on a symmetric space, Proc. Japan Acad., t. 53, 1977, p. 237-241. | DOI | MR | Zbl
and . -[9] Distributions sphériques sur les espaces hyperboliques, J. Math. Pures Appl., t. 58, 1979, p. 369-444. | MR | Zbl
. -[10] Espaces symétriques à groupe foundamental simple non compact, Dokl. Akad. Nauk, SSSR, t. 108, 1956, p. 1026-1028. | MR | Zbl
. -[11] Discrete series for semisimple symmetric spaces, Ann. of Math., t. 111 , 1980, p. 253-311. | DOI | MR | Zbl
. -[11a] Analysis on non-Riemannian Symmetric Spaces, Providence, R.I., CBMS Monogr. Amer. Math. Soc. (to appear). | MR | Zbl
. -[12] Spherical functions on symmetric spaces, Dokl. Akad. Nauk, SSSR, t. 70, 1950, p. 5-8, Amer. Math. Soc. Transl, t. 37 1964, p. 39-44. | MR | Zbl
. -[13] Generalized Functions, Vol. 5. - Academic Press, 1966. | MR | Zbl
, and . -[14] Unitary representations of the unimod-ular group containing the identity representation of the unitary subgroup, Trudy Moscov. Mat. Obsc., t. 1, 1952, p. 423-475. | MR | Zbl
and . -[15] Plancherel measure of Riemannian symmetric spaces of non-positive curvature, Dokl. Akad. Nauk. SSSR, t. 145, 1962, p. 252-255. | MR | Zbl
and . -[16] Introduction aux travaux de A. Selberg. - Séminaire Bourbaki, t. 144, 1957. | EuDML | Numdam | MR | Zbl
. -[17] Spherical functions on a semisimple Lie group, I, II, Amer. J. Math., t. 80, 1958, p. 241-310 ; p. 553-613. | DOI | MR | Zbl
. -[18] Discrete series for semisimple Lie groups, II, Acta Math., t. 116, 1966, p. 1-111. | DOI | MR | Zbl
. -[19] Radon-Fourier transforms on symmetric spaces and related group representations, Bull. Amer. Math. Soc., t. 71, 1965, p. 757-763. | DOI | MR | Zbl
-[20] A duality for symmetric spaces with applications to group representations, Adv. in Math., t. 5, 1970, p. 1-154. | DOI | MR | Zbl
. -[21] The surjectivity of invariant differential operators on symmetric spaces, Ann. of Math., t. 98, 1973, p. 451-480. | DOI | MR | Zbl
. -[22] Eigenspaces of the Laplacian ; integral representations and irreducibility, J. Funct. Anal., t. 17, 1974, p. 328-353. | DOI | MR | Zbl
. -[23] A duality for symmetric spaces with applications to group representations, II. Differential equations and eigenspace representations, Adv. in Math, t. 22, 1976, p. 187-219. | DOI | MR | Zbl
. -[24] Eigenfunctions of invariant differential operators on a symmetric space, Ann. of Math., t. 107, 1978, p. 1-39. | DOI | MR | Zbl
, , , , and . -[25] Spherical distributions on rank one symmetric spaces. Proefschrift, University of Leiden, 1983.
. -[25a] The Plancherel formula for a symplectic symmetric space. Report 27, Math. Inst. Univ. Leiden, 1984.
. -[26] Eigenfunction expansions associated with the second-order invariant operator on hyperboloids and cones III, J. Math. Phys., t. 8, 1967, p. 1079-1093. | DOI | MR | Zbl
, and . -[27] Analogue of the Plancherel formula for hyperboloids, Soviet Math. Dokl, t. 9, 1968, p. 1382-1385. | Zbl
. -[28] Representations of pseudo-orthogonal groups associated with a cone, Mat. Sb. USSR, t. 10, 1970, p. 333-347. | DOI
. -[29] Die Darstellungsreihe zu einem affinen symmetrischen Raum. Preprint, Univ. of Iceland, 1983.
. -[30] Fourier analysis on semisimple symmetric spaces, in Non-Commutative Harmonie Analysis and Lie Groups, p. 357-369. - Berlin, Springer-Verlag 1981, (Lecture Notes in Math, 880). | DOI | Zbl
. -[31] A description of discrete series for semisimple symmetric spaces. Advanced Studies in Pure Math. (to appear). | MR | Zbl
and . -[32] Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Math. Ann., t. 97, 1927, p. 737-755. | DOI | EuDML | JFM | MR
and . -[33] Analysis on real hyperbolic spaces, J. Funct. Anal., t. 30, 1978, p. 448-477. | DOI | MR | Zbl
. -[34] The Plancherel formula for , Sci. Papers College Gen. Ed. Univ. Tokyo, t. 30, 1980, p. 93-105. | MR | Zbl
and . -[35] Hyperfunctions and Harmonic Analysis on Symmetric Spaces. - Boston, Birkhäuser, 1984. | DOI | MR | Zbl
. -[36] A series of unitary irreducible representations induced from a symmetric subgroup of a semisimple Lie group, Invent. Math., t. 68, 1982, p. 497-516. | DOI | EuDML | MR | Zbl
. -[37] Fourier analysis on the sphere, Trans. Amer. Math. Soc., t. 209, 1975, p. 1-31. | DOI | MR | Zbl
. -[38] Fourier analysis on compact symmetric space, Bull. Amer. Math. Soc., t. 83, 1977, p. 378-380. | DOI | MR | Zbl
. -[39] On the decomposition of the regular representation of the Lorentz group on a hyperboloid of one sheet, Proc. Japan Acad., t. 43, 1967, p. 1-5. | DOI | MR | Zbl
. -[40] On mean convergence of Fourier series on compact Lie groups, Trans. Amer. Math. Soc., t. 218, 1976, p. 61-87. | DOI | MR | Zbl
. -[41] Harmonic analysis on hyperboloids, J. Funct. Anal., t. 12, 1973, p. 341-383. | DOI | MR | Zbl
. -[42] Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula (to appear). | MR | Zbl
. -[42a] Elementary spherical functions on symmetric spaces, Math. Scand., t. 39, 1976, p. 343-358. | DOI | EuDML | MR | Zbl
. -[42b] On a recursion formula for elementary spherical functions on symmetric spaces and its applications, Math. Scand., t. 41, 1977, p. 99-112. | DOI | EuDML | MR | Zbl
. -[43] Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen. III, Math. Z., t. 24, 1926, p. 377-395. | DOI | EuDML | JFM | MR
. -[44] Spaces of Constant Curvature. - New-York, McGraw-Hill, 1967. | MR | Zbl
. -