Spherical functions and spectral synthesis
Meaney, Christopher
Compositio Mathematica, Tome 56 (1985), p. 311-329 / Harvested from Numdam
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Publié le : 1985-01-01
@article{CM_1985__54_3_311_0,
     author = {Meaney, Christopher},
     title = {Spherical functions and spectral synthesis},
     journal = {Compositio Mathematica},
     volume = {56},
     year = {1985},
     pages = {311-329},
     mrnumber = {791505},
     zbl = {0579.43008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1985__54_3_311_0}
}

Meaney, Christopher. Spherical functions and spectral synthesis. Compositio Mathematica, Tome 56 (1985) pp. 311-329. http://gdmltest.u-ga.fr/item/CM_1985__54_3_311_0/

[1] K. Aomoto: Sur les transformations d'horisphere et les equations integrales qui s'y rattachent. J. Fac. Sci. Univ. of Tokyo 14 (1967) 1-23. | MR 222218 | Zbl 0177.41801

[2] D. Barlet and J.L. Clerc: Le comportement à l'infini des fonctions de Bessel généralisées. I. Preprint, Institut Elie Cartan, Nancy, (Jan. 1981).

[3] F. Cazzaniga and C. Meaney: A local property of absolutely convergent Jacobi polynomial series. Tôhoku Math. J. 34 (1982) 389-406. | MR 676117 | Zbl 0492.42011

[4] A.K. Chilana and K.A. Ross: Spectral synthesis in hypergroups. Pacific J. Math. 76 (2) (1978) 313-328. | MR 622041 | Zbl 0351.43009

[5] J.L. Clerc: Le comportement à l'infini des fonctions de Bessel généralisées. II. Preprint. Institut Elie Cartan, Nancy, Jan. 1981. | MR 611408

[6] J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan: Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups. Comp. Math. 49 (1983) 309-398. | Numdam | MR 707179 | Zbl 0524.43008

[7] M. Eguchi and K. Kumahara: An Lp Fourier analysis on symmetric spaces. J. Functional Anal. 47 (1982) 230-246. | MR 664337 | Zbl 0493.43006

[8] P. Eymard: L'algèbre de Fourier d'une groupe localement compact. Bull. Soc. Math. France. 92 (1964) 181-236. | Numdam | MR 228628 | Zbl 0169.46403

[9] P. Eymard: Algèbres Ap et convoluteurs de LP. Sém. Bourbaki no. 367 (1969). | Numdam | Zbl 0264.43006

[10] M. Flensted-Jensen: Paley-Wiener type theorems for a differential operator connected with symmetric spaces. Ark. Mat. 10 (1972) 143-162. | MR 318974 | Zbl 0233.42012

[11] M. Flensted-Jensen and T. Koornwinder: The convolution structure for Jacobi function expansions. Ark. Mat. 11 (1973) 245-262. | MR 340938 | Zbl 0267.42009

[12] M. Flensted-Jensen and T. Koornwinder: Jacobi funtions: the addition formula and the positivity of the dual convolution structure. Ark. Mat. 17 (1979) 139-151. | MR 543509 | Zbl 0409.33009

[13] M. Flensted-Jensen and D.L. Ragozin: Spherical functions and Fourier transforms of L1-functions. Ann. Sci. Éc. Norm. Sup. 6 (1973) 457-458. | Numdam | MR 364553 | Zbl 0293.22020

[14] R. Gangolli: On the Placherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups. Ann. Math. 93 (1971) 150-165. | MR 289724 | Zbl 0232.43007

[15] M. Gatesoupe: Caractérisation locale de la sous algèbre fermée des fonctions radiales de F L1(Rn). Ann. Inst. Fourier, Grenoble. 17 (1967) 93-107. | Numdam | MR 222559 | Zbl 0171.10201

[16] E. Hahn: Asymptotik bei Jacobi-Polynomen und Jacobi-Functionen. Math. Z. 171 (1980) 201-226. | MR 575239 | Zbl 0411.33008

[17] Harish-Chandra: Spherical functions on a semisimple Lie group, I. Amer. J. Math. 80 (1958) 241-310. | MR 94407 | Zbl 0093.12801

[18] Y. Hasegawa: On the integrability of Fourier-Jacobi transforms. Ark. Mat. 16 (1978) 127-139. | MR 493151 | Zbl 0382.42009

[19] S. Helgason: Differential geometry, Lie groups, and symmetric spaces. Academic Press, New York, San Francisco, London (1978). | MR 514561 | Zbl 0451.53038

[20] C. Herz: Spectral synthesis for the circle. Ann. of Math. 68 (1958) 709-712. | MR 100758 | Zbl 0084.09703

[21] C. Herz: La rapport entre l'algèbre Ap d'un groupe et d'un sous-groupe C.R. Acad. Sci. Paris 271 (1970) 244-246. | MR 273428 | Zbl 0195.13803

[22] C. Herz: Harmonic synthesis for subgroups. Ann. Inst. Fourier. Grenoble. 23 (3) (1973) 91-123. | Numdam | MR 355482 | Zbl 0257.43007

[23] B. Hoogenboom: Spherical functions and invariant differential operators on complex Grassmann manifolds. Ark. Mat. 20 (1982) 69-85. | MR 660126 | Zbl 0496.33010

[24] W. Kirsch and D. Müller: On the synthesis problem for orbits of Lie groups in Rn. Ark. Mat. 18 (1980) 145-155. | MR 608333 | Zbl 0478.43004

[25] T. Koornwinder: A new proof of a Paley-Wiener type theorem for the Jacobi transform. Ark. Mat. 13 (1975) 145-158. | MR 374832 | Zbl 0303.42022

[26] F. Mayer-Lindenberg: Zur Dualitätstheorie symmetrischer Paare. J. für die reine und angew. Math. 321 (1981) 36-52. | MR 597978 | Zbl 0438.22004

[27] C. Meaney: On the failure of spectral synthesis for compact semisimple Lie groups. J. Functional Anal. 48 (1982) 43-57. | MR 671314 | Zbl 0486.43005

[28] M. Mizony: Contribution à l'analyse harmonique spherique. Publ. Dépt. Math. Lyon 12-1 (1975) 61-108. | Numdam | MR 383011 | Zbl 0313.43019

[29] M. Mizony: Transformation de Laplace-Jacobi, Preprint, Dépt. Math., Univ. Claude Bernard, Lyon (May 1981).

[30] F. Ricci: Local properties of the central Wiener algebra on the regular set of a compact Lie group. Bull. Sc. Math. 101 (1977) 87-95. | MR 481937 | Zbl 0358.43001

[31] I.J. Schoenberg: Metric spaces and completely monotone functions. Ann. Math. 39 (1938) 811-841. | JFM 64.0617.03 | MR 1503439 | Zbl 0019.41503

[32] A. Schwartz: The smoothness of Hankel transforms. J. Math. Anal. Appl. 28 (1969) 500-507. | MR 249963 | Zbl 0167.12401

[33] A. Schwartz: The structure of the algebra of Hankel transforms and the algebra of Hankel-Stieltjes transforms. Can. J. Math. 23 (1971) 236-246. | MR 273312 | Zbl 0214.13201

[34] R.J. Stanton and P.A. Tomas: Expansions for spherical functions on noncompact symmetric spaces. Acta Math. 140 (1978) 251-276. | MR 511124 | Zbl 0411.43014

[35] G. Warner: Harmónic analysis on semi-simple Lie groups I. Springer-Verlag, New York, Heidelberg, Berlin (1972). | MR 498999 | Zbl 0265.22020

[36] E.T. Whittaker and G.N. Watson: A course of modern analysis. Cambridge University Press (1927). | JFM 45.0433.02 | MR 1424469