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Arthur, James

A Paley-Wiener theorem for real reductive groups. (English) Zbl 0514.22006

Acta Math. 150, 1-89 (1983).
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scan of Zbl 0514.22006

Cited in 3 Reviews
Cited in 42 Documents

MSC:

22E30 Analysis on real and complex Lie groups
43A80 Analysis on other specific Lie groups

Keywords:

reductive Lie group; Paley-Wiener problem; Fourier transform; tau- spherical function; Hecke algebra; Eisenstein integrals; Plancherel formula
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References:

[1] Campoli, O.,The complex Fourier transform on rank one semisimple Lie groups. Thesis, Rutgers University, 1977.
[2] Casselman, W., Jacquet modules for real reductive groups.Proc. Int. Cong. Math., Helsinki, 1978, 557–563.
[3] Casselman, W., The Bruhat filtration of principal series. In preparation. · Zbl 0472.22004
[4] Cohn, L.,Analytic theory of Harish-Chandra’s C-function. Lecture Notes in Mathematics, 429, Springer-Verlag. · Zbl 0342.33026
[5] Delorme, P., Théorème de type Paley-Wiener pour les groupes de Lie semisimples réels avec une seule classe de conjugaison de sous-groupes de Cartan. Preprint. · Zbl 0517.22011
[6] Ehrenpreis, L. &Mautner, F. I., Some properties of the Fourier transform on semisimple Lie groups I.Ann. of Math., 61 (1955), 406–439. · Zbl 0066.35701 · doi:10.2307/1969808
[7] –, Some properties of the Fourier transform on semisimple Lie groups, II.Trans. Amer. Math. Soc., 84 (1957), 1–55. · Zbl 0079.13201
[8] Gangolli, R., On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups.Ann. of Math., 93 (1971), 150–165. · Zbl 0232.43007 · doi:10.2307/1970758
[9] Harish-Chandra, Some results on differential equations. Manuscript (1960). · Zbl 0161.33803
[10] Harish-Chandra, Differential equations and semisimple Lie groups. Manuscript (1960). · Zbl 0080.10202
[11] – Harmonic analysis on real reductive groups, I.J. Funct. Anal., 19 (1975), 104–204. · Zbl 0315.43002 · doi:10.1016/0022-1236(75)90034-8
[12] – Harmonic analysis on real reductive groups II.Invent. Math., 36 (1976), 1–55. · Zbl 0341.43010 · doi:10.1007/BF01390004
[13] –, Harmonic analysis on real reductive groups, III.Ann. of Math., 104 (1976), 117–201. · Zbl 0331.22007 · doi:10.2307/1971058
[14] Helgason, S., An analog of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces.Math. Ann., 165 (1966), 297–308. · Zbl 0178.17101 · doi:10.1007/BF01344014
[15] – A duality for symmetric spaces with applications to group representations.Adv. in Math., 5 (1970), 1–154. · Zbl 0209.25403 · doi:10.1016/0001-8708(70)90037-X
[16] – The surjectivity of invariant differential operators on symmetric spaces I.Ann. of Math., 98 (1973), 451–479. · Zbl 0274.43013 · doi:10.2307/1970914
[17] – A duality for symmetric spaces with applications to group representations II.Adv. in Math., 22 (1976), 187–210. · Zbl 0351.53037 · doi:10.1016/0001-8708(76)90153-5
[18] Johnson, K. D., Differential equations and an analogue of the Paley-Wiener theorem for linear semisimple Lie groups.Nagoya Math. J., 64 (1976), 17–29. · Zbl 0329.43008
[19] Kawazoe, T., An analogue of Paley-Wiener theorem on semisimple Lie groups and functional equations for Eisenstein integrals.Tokyo J. Math., 3 (1980), 219–248. · Zbl 0455.43007 · doi:10.3836/tjm/1270472995
[20] Kawazoe, T. An analogue of Paley-Wiener theorem on semi-simple Lie groups and functional equations for Eisenstein integrals. Preprint.
[21] Langlands, R. P., On the classification of irreducible representations of real algebraic groups. Preprint. · Zbl 0741.22009
[22] Langlands, R. P.,On the functional equations satisfied by Eisenstein series. Lecture Notes in Mathematics, 544 (1976). · Zbl 0332.10018
[23] Wallach, N., On Harish-Chandra’s generalizedC-functions.Amer. J. Math., 97 (2) 1975, 386–403. · Zbl 0312.22010 · doi:10.2307/2373718
[24] Warner, G.,Harmonic analysis on semisimple Lie groups II. Springer-Verlag, Berlin, New York, 1972. · Zbl 0265.22021
[25] Zelobenko, D. P., Harmonic analysis on complex semisimple Lie groups.Proc. Int. Cong. Math., Vancouver, 1974, Vol. II, 129–134. · Zbl 0283.22010
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