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Eigenspaces of the Laplacian ; integral representations and irreducibility. (English) Zbl 0303.43021

MSC:
43A85 Harmonic analysis on homogeneous spaces
47B99 Special classes of linear operators
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[1] Boas, R.P, Entire functions, (1954), Academic Press New York
[2] Erdélyi, A, ()
[3] Harish-Chandra, Spherical functions on a semisimple Lie group I, Amer. J. math., 80, 241-310, (1958) · Zbl 0093.12801
[4] Hashizume, M; Kowata, A; Minemura, K; Okamoto, K, An integral representation of an eigenfunction of the Laplacian on the Euclidean space, Hiroshima math. J., 2, 535-545, (1972) · Zbl 0269.35012
[5] Hashizume, M; Minemura, K; Okamoto, K, Harmonic functions on Hermitian hyperbolic spaces, Hiroshima math. J., 3, 81-108, (1973) · Zbl 0273.31011
[6] Helgason, S; Helgason, S; Helgason, S; Helgason, S; Helgason, S, The eigenfunctions of the Laplacian on a two-point homogeneous space; integral representations and irreducibility, (), 98, 451-479, (1973) · Zbl 0274.43013
[7] {\scK. D. Johnson}, Composition series and intertwining operators for the spherical principal series II (to appear).
[8] {\scK. D. Johnson and N. Wallach}, Composition series and intertwining operators for the spherical principal series (preprint). · Zbl 0257.22016
[9] Kostant, B, On the existence and irreducibility of certain series of representations, Bull. amer. math. soc., 75, 627-642, (1969) · Zbl 0229.22026
[10] Köthe, G, Die randverteilungen analytischer funktionen, Math. Z., 57, 13-33, (1952) · Zbl 0047.35203
[11] Lions, J.L; Magenes, E, Problèmes aux limites non homogènes (VII), Ann. math. pura appl. 4, 63, 201-224, (1963) · Zbl 0126.31103
[12] {\scK. Minemura}, Eigenfunctions of the Laplacian on a real hyperbolic space J. Math. Soc. Japan (to appear).; {\scK. Minemura}, Eigenfunctions of the Laplacian on a hermitian hyperbolic space (preprint). · Zbl 0274.31004
[13] Roumieu, C, Ultra-distributions définies sur rn et sur certaines classes de variétés differentiables, J. analyse math., X, 153-192, (1962-1963) · Zbl 0122.34802
[14] Seeley, R, Eigenfunction expansion of analytic functions, (), 734-738 · Zbl 0183.10102
[15] Vilenkin, N.J, Special functions and the theory of group representations, (1968), Amer. Math. Soc Providence, R.I
[16] Warner, G, ()
[17] Weil, A, L’intégration dans LES groupes topologiques et LES applications, (1940), Hermann Pari · Zbl 0063.08195
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