Published: 1975 Received: July 03, 1973Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Wrong : 1) H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., 68 (1958), 460-472. 2) Harish-Chandra, Spherical functions on a semisimple Lie group I, Amer. J. Math., 80 (1958), 241-310. 3) M. Hashizume, A. Kowata, K. Minemura and K. Okamoto, An integral representation of an eigenfunction of the laplacian on the euclidean space, Hiroshima Math. J., 2 (1972), 535-545. 4) M. Hashizume, K. Minemura and K. Okamoto, Harmonic functions on hermitian hyperbolic spaces, Hiroshima Math. J., 3 (1973), 81-108. 5) S. Helgason, A duality for symmetric spaces with applications to group representations, Advances in Math., 5 (1970), 1-154. 6) S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. 7) K. Jhonson and N. R. Wallach, Composition series and intertwining operators for the spherical principal series, Bull. Amer. Math. Soc., 78 (1972), 1053-1059. 8) A. W. Knapp, Fatou's theorem for symmetric spaces: I, Ann. of Math., 88 (1968), 106-127. 9) B. Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc., 75 (1969), 627-642. 10) A. Kowata and K. Okamoto, Harmonic functions and the Borel-Weil theorem, to appear in Hiroshima Math. J. 11) N. N. Lebedev, Special Functions and Their Applications, Prentice-Hall, London, 1965. 12) J. L. Lions and E. Magenes, Problèmes aux limites non homogènes (VII), Ann. Math. Pura Appl., 4 (1963), 201-224. 13) A. Martineau, Distributions et valeurs au bords des fonctions holomorphes, Theory of Distributions (Proc. Internat. Summer Inst.), Lisbon, 1964, 193-326. 14) A. Martineau, Les hyperfonctions de M. Sato, Séminaire Bourbaki, 13 (1960/1), No. 214. 15) K. Minemura, Harmonic functions on real hyperbolic spaces, Hiroshima Math. J., 3 (1973), 121-151. 16) K. Okamoto, Harmonic Analysis on homogeneous vector bundles, Lecture notes in Math., Springer-Verlag, 266 (1972), 255-271. 17) A. Orihara, Bessel functions and the euclidean motion group, Tohoku Math. J., 13 (1961), 66-74. 18) M. Sato, Theory of hyperfunctions II, J. Fac. Sci. Univ. Tokyo, 8 (1960), 387-436. 19) M. Sugiura, Fourier series of smooth functions on compact Lie groups, Osaka J. Math., 8 (1971), 33-47. 20) R. Takahashi, Sur les représentations unitaires des groupes de Lorentz généralisés, Bull. Soc. Math. France, 91 (1963), 289-433.
Right : [1] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., 68 (1958), 460-472. [2] Harish-Chandra, Spherical functions on a semisimple Lie group I, Amer. J. Math., 80 (1958), 241-310. [3] M. Hashizume, A. Kowata, K. Minemura and K. Okamoto, An integral representation of an eigenfunction of the laplacian on the euclidean space, Hiroshima Math. J., 2 (1972), 535-545. [4] M. Hashizume, K. Minemura and K. Okamoto, Harmonic functions on hermitian hyperbolic spaces, Hiroshima Math. J., 3 (1973), 81-108. [5] S. Helgason, A duality for symmetric spaces with applications to group representations, Advances in Math., 5 (1970), 1-154. [6] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. [7] K. Jhonson and N. R. Wallach, Composition series and intertwining operators for the spherical principal series, Bull. Amer. Math. Soc., 78 (1972), 1053-1059. [8] A. W. Knapp, Fatou's theorem for symmetric spaces: I, Ann. of Math., 88 (1968), 106-127. [9] B. Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc., 75 (1969), 627-642. [10] A. Kowata and K. Okamoto, Harmonic functions and the Borel-Weil theorem, to appear in Hiroshima Math. J. [11] N. N. Lebedev, Special Functions and Their Applications, Prentice-Hall, London, 1965. [12] J. L. Lions and E. Magenes, Problèmes aux limites non homogènes (VII), Ann. Math. Pura Appl., 4 (1963), 201-224. [13] A. Martineau, Distributions et valeurs au bords des fonctions holomorphes, Theory of Distributions (Proc. Internat. Summer Inst.), Lisbon, 1964, 193-326. [14] A. Martineau, Les hyperfonctions de M. Sato, Séminaire Bourbaki, 13 (1960/1), No. 214. [15] K. Minemura, Harmonic functions on real hyperbolic spaces, Hiroshima Math. J., 3 (1973), 121-151. [16] K. Okamoto, Harmonic Analysis on homogeneous vector bundles, Lecture notes in Math., Springer-Verlag, 266 (1972), 255-271. [17] A. Orihara, Bessel functions and the euclidean motion group, Tôhoku Math. J., 13 (1961), 66-74. [18] M. Sato, Theory of hyperfunctions II, J. Fac. Sci. Univ. Tokyo, 8 (1960), 387-436. [19] M. Sugiura, Fourier series of smooth functions on compact Lie groups, Osaka J. Math., 8 (1971), 33-47. [20] R. Takahashi, Sur les représentations unitaires des groupes de Lorentz généralisés, Bull. Soc. Math. France, 91 (1963), 289-433.
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