Nagoya Mathematical Journal

Eigenspaces of the Laplace-Beltrami operator on a hyperboloid

Jirō Sekiguchi

Source: Nagoya Math. J. Volume 79 (1980), 151-185.

Primary Subjects: 22E30
Secondary Subjects: 43A85, 58G07

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.nmj/1118786176
Mathematical Reviews number (MathSciNet): MR0587417
Zentralblatt MATH identifier: 0468.35074

References

[1] J.Faraut, Distributions spheriques sur les espace pseudo-Riemanniens etles hyper- boloides (preprint).
Mathematical Reviews (MathSciNet): MR566654
Zentralblatt MATH: 0436.43011
[2] I.M.Gefand and G.E. Shilov, Generalized functions, vol.1,1964,Academic Press, New York and London.
[3] Harish-Chandra, Spherical functions ona semisimple Lie group I,Amer. J.Math., 80 (1958),241-310.
Mathematical Reviews (MathSciNet): MR0094407
Zentralblatt MATH: 0093.12801
[4] S.Helgason, Aduality for symmetric spaces with applications togroup representa- tions, Advances in Math., 5 (1970), 1-154.
Mathematical Reviews (MathSciNet): MR0263988
Zentralblatt MATH: 0209.25403
[5] S. Helgason, Invariant differential equations on homogeneous manifolds, Bull. Amer. Math. Soc. vol.83 (1977), 751-774.
Mathematical Reviews (MathSciNet): MR0445235
Zentralblatt MATH: 0377.43009
[6] M. Kashiwara, K. Kowata, K. Minemura, K. Okamoto, T. Oshima, and M. Tanaka, Eigenfunctions of invariant differential operators on a symmetric space, Ann. of Math., 107 (1978), 1-39.
Mathematical Reviews (MathSciNet): MR485861
Zentralblatt MATH: 0377.43012
[7] M. Kashiwara and T. Oshima, Systems of differential equations with regular singu- larities and their boundary value problems, Ann. of Math., 106 (1977), 145-200.
Mathematical Reviews (MathSciNet): MR0482870
Zentralblatt MATH: 0358.35073
[8] S. S. Koh, On affine symmetric spaces, Trans. Amer. Math. Soc, 119 (1965), 291- 309.
Mathematical Reviews (MathSciNet): MR0184170
Zentralblatt MATH: 0139.39502
[9] T. Matsuki, The orbits of affine symmetric spaces under the action of minimal para- bolic subgroups, J. Math. Soc. Japan, 31, No.2 (1979), 331-357.
Mathematical Reviews (MathSciNet): MR527548
Zentralblatt MATH: 0396.53025
[10] S. Matsumoto, K. Hiraoka and K. Okamoto, Eigenfunctions of the laplacian on a real hyperboloid of one sheet, Hiroshima Math. J., 7 (1978), 855-864.
Mathematical Reviews (MathSciNet): MR0622203
Zentralblatt MATH: 0389.35015
[11] K. Minemura, Eigenfunctions of the laplacian on a real hyperbolic space, J. Math. Soc. Japan, 27 (1975), 82-105.
Mathematical Reviews (MathSciNet): MR0382549
Zentralblatt MATH: 0292.35023
[12] T. Oshima, Boundary value problem for symmetric spaces corresponding to various boundaries, RIMS Kkyroku, 281 (1976), 211-226 (in Japanese).
[13] T. Oshima, On a realization of Riemannian symmetric spaces, J. Math. Soc. Japan, 30 (1978), 117-132.
Mathematical Reviews (MathSciNet): MR0477175
Zentralblatt MATH: 0364.43010
[14] T. Oshima and J. Sekiguchi, Eigenspace of invariant differential operators on an affine symmetric space, preprint.
Mathematical Reviews (MathSciNet): MR564184
Zentralblatt MATH: 0434.58020
[15] W. Rossmann, Analysis on real hyperbolic spaces, J. Functional Analysis, 30 (1978), 448-477.
Mathematical Reviews (MathSciNet): MR518343
Zentralblatt MATH: 0467.43006
[16] N. R. Wallach, Harmonic analysis on homogeneous spaces, Marcel Dekker, Inc., New York. Department of Mathematics Tokyo Metropolitan University
Mathematical Reviews (MathSciNet): MR0498996

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