Hiroshima Mathematical Journal

An integral representation of an eigenfunction of invariant differential operators on a symmetric space

Toru Inoue, Kiyosato Okamoto, and Makoto Tanaka

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 4, Number 2 (1974), 413-419.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206137071

Digital Object Identifier
doi:10.32917/hmj/1206137071

Mathematical Reviews number (MathSciNet)
MR0364550

Zentralblatt MATH identifier
0293.58016

Subjects
Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 43A85: Analysis on homogeneous spaces

Citation

Inoue, Toru; Okamoto, Kiyosato; Tanaka, Makoto. An integral representation of an eigenfunction of invariant differential operators on a symmetric space. Hiroshima Math. J. 4 (1974), no. 2, 413--419. doi:10.32917/hmj/1206137071. https://projecteuclid.org/euclid.hmj/1206137071


Export citation

References

  • [1] M. Eguchi, M. Hashizume and K. Okamoto, The Paley-Wiener theorem for distributions on symmetric spaces, Hiroshima Math. J. 3 (1973), 109-120.
  • [2] L. Ehrenpreis, Some propertiesof distributiosnon Lie groups, Pacific J. Math. 6 (1956), 591-605.
  • [3] L. Ehrenpreis, A fundamental principle for systems of linear differential equationswith constant coefficients, and some of its applications, Proc. Intern. Symp. on Linear Spaces, Jerusalem, (1961), 161-174.
  • [4] L. Ehrenpreis, Analytically uniform spaces and some applications, Trans. Amer. Math. Soc. 101 (1961), 52-74.
  • [5] L. Ehrenpreis, Fourier analysis in several complex variables, Wiley-Interscience, New York, 1970.
  • [6] Harish-Chandra, Spherical functions on a semisimple Lie group, /, //, Amer. J. Math. 80 (1958), 241-310, 553-613.
  • [7] 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.
  • [8] S. Helgason, A dualityfor symmetric spaces with applications to group representations, Advances in Mathematics 5 (1970), 1-154.
  • [9] S. Helgason, The surjectivity of invariant differential operators on symmetric spaces I, Ann. of Math, (to appear).
  • [10] S. Helgason, The eigenfunctions of the Laplacian on a two-point homogeneous space, Amer. Math. Soc. Summer Institute Stanford, (1973).
  • [11] J. Horvath, Topological vector spaces and distributions, I, Addison-Wesley Publishing Company, 1966.
  • [12] A. Kowata and K. Okamoto, Homogeneous harmonic polynomials and the Borel-Weil theorem,Hiroshima Math. J. (to appear).
  • [13] L. Schwartz, Thorie des distributions, I, II, Hermann, Paris, 1957.