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Orbital Integrals and the Wave Operator for Isotropic Lorentz Spaces

  • Sigurdur Helgason
Part of the Progress in Mathematics book series (PM, volume 5)

Abstract

In Chapter II, §3 we discussed the problem of determining a function on a homogeneous space by means of its integrals over generalized spheres. We shall now solve this problem for the isotropic Lorentz spaces (Theorem 4.1 below). As we shall presently explain these spaces are the Lorentzian analogs of the two-point homogeneous spaces considered in Chapter III.

Keywords

Wave Operator Isotropy Subgroup Riemannian Structure Lorentzian Structure Bibliographical Note 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. Borovikov, W.A. Fundamental solutions of linear partial differential equations with constant coefficients, Trudy Moscov. Mat. Obshch. 8 (1959), 199–257.MathSciNetzbMATHGoogle Scholar
  2. Garding, L. Transformation de Fourier des distributions homogènes, Bull. Soc. Math. France 89 (1961), 381–428.MathSciNetzbMATHGoogle Scholar
  3. Gelfand, I.M. and Graev, M.I. Analogue of the Plancherel formula for the classical groups, Trudy Moscov. Mat. Obshch. 4 (1955), 375–404.MathSciNetGoogle Scholar
  4. Lax, P. and Phillips, R.S., Scattering Theory, Academic Press, New York, 1967.zbMATHGoogle Scholar
  5. Nagano, T. Homogeneous sphere bundles and the isotropic Riemannian manifolds, Nagoya Math. J. 15 (1959), 29–55.MathSciNetzbMATHGoogle Scholar
  6. Nievergelt, Y. “Radon transforms satisfying the Bolker assumtion,” in: Proc. Conf. 75 Years of Radon Transform, Vienna, 1992, International Press, Hong Kong, 1994, 231–244.Google Scholar
  7. Wiegerinck, J.J.O.O. A support theorem for the Radon transform on Rn, Nederl. Akad. Wetensch. Proc. A 88 (1985), 87–93.MathSciNetCrossRefGoogle Scholar
  8. Boman, J. and Quinto, E.T. Support theorems for real-analytic Radon transforms, Duke Math. J. 55 (1987), 943–948.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Bouaziz, A. Formule d’inversion des intégrales orbitales sur les groupes de Lie réductifs, J. Funct. Anal. 134 (1995), 100–182.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Flicker, Y.Z. Orbital integrals on symmetric spaces and spherical characters, J. Algebra 184 (1996), 705–754.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Quinto, E.T. Morera theorems for complex manifolds, preprint, 1998.Google Scholar
  12. Ishikawa, S. The range characterization of the totally geodesic Radon transform on the real hyperbolic space, Duke Math. J. 90 (1997), 149–203.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Sigurdur Helgason 1999

Authors and Affiliations

  • Sigurdur Helgason
    • 1
  1. 1.Department of MathematicsMITCambridgeUSA

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