Spherical functions and spectral synthesis
Compositio Mathematica, Tome 54 (1985) no. 3, pp. 311-329.
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     author = {Meaney, Christopher},
     title = {Spherical functions and spectral synthesis},
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     pages = {311--329},
     publisher = {Martinus Nijhoff Publishers},
     volume = {54},
     number = {3},
     year = {1985},
     mrnumber = {791505},
     zbl = {0579.43008},
     language = {en},
     url = {http://www.numdam.org/item/CM_1985__54_3_311_0/}
}
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Meaney, Christopher. Spherical functions and spectral synthesis. Compositio Mathematica, Tome 54 (1985) no. 3, pp. 311-329. http://www.numdam.org/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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

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

[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 | Zbl

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

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

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

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

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

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

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