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Lie Group Representations III pp 254–287Cite as

Wave equations on homogeneous spaces

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Bibliography

  1. L. Àsgeirsson, Über eine Mitterwertseigenschaft von Lösungen homogener linearer partieller Differentialgleichung 2. Ordnung mit konstanten Koefficienten. Math. Ann. 113(1936), 321–346.

    Article  MATH  Google Scholar 

  2. J. Beem and P. Ehrlich, Global Lorentzian Geometry, Marcel Dekker, New York 1981.

    MATH  Google Scholar 

  3. C.L. Fefferman, Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains. Ann. of Math. 103(1976), 395–416.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Freudenthal and de Vries, H. Linear Lie Groups. Academic Press, 1969.

    Google Scholar 

  5. F.C. Friedlander, The Wave Equation in Curved Space-Time. Cambridge Univ. Press, 1975.

    Google Scholar 

  6. P. Günther, Über einige spezielle Probleme aus der Theorie der linearen partiellen Differentialgleichungen zweiter Ordnung. Ber. Verh. Sächs. Akad. Wiss. Leipzig 102(1957), 1–50.

    MATH  Google Scholar 

  7. _____, Ein Beispiel einer nichttrivialen Huygensschen Differentialgleichung mit vier unabhängigen Variablen. Arch. Rat. Mech. Anal. 18(1965), 103–106.

    Article  MATH  Google Scholar 

  8. J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, 2nd Ed. Dover 1952.

    Google Scholar 

  9. Harish-Chandra, Differential operators on a semisimple Lie algebra. Amer. J. Math. 79(1957), 87–120.

    Article  MathSciNet  MATH  Google Scholar 

  10. _____, Spherical Functions on a semisimple Lie group. Amer. J. Math. 80(1958), 241–310.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Helgason, Partial differential equations on Lie groups. Scand. Math. Congress XIII, Helsinki 1957, 110–115.

    Google Scholar 

  12. _____, Differential operators on homogeneous spaces. Acta Math. 102(1959), 239–299.

    Article  MathSciNet  MATH  Google Scholar 

  13. _____, Some remarks on the exponential mapping for an affine connection. Math. Scand. 9(1961), 129–146.

    MathSciNet  MATH  Google Scholar 

  14. _____, Fundamental solutions of invariant differential operators on symmetric spaces. Amer. J. Math. 86(1964), 565–601.

    Article  MathSciNet  MATH  Google Scholar 

  15. _____, Analysis on Lie Groups and Homogeneous Spaces. Conf. Board Math. Sci. Series, No. 14, Amer. Math. Soc. Providence, 1972.

    Google Scholar 

  16. _____, Solvability questions for invariant differential operators, pp.517–527, in Proc. 5th Int. Colloq. on "Group Theoretical Methods in Physics" Montreal 1976, Academic Press 1977.

    Google Scholar 

  17. _____, Differential Geometry, Lie Groups and Symmetric Spaces. Academic Press, 1978.

    Google Scholar 

  18. E. Hölder, Poissonsche Wellenformel in nichteuclidischen Räumen. Ber. Verh. Sächs. Akad. Wiss. Leipzig 90(1938), 55–66.

    MATH  Google Scholar 

  19. F. John, Plane Waves and Spherical Means. Interscience, New York, 1955.

    MATH  Google Scholar 

  20. I.A. Kiprijanov, and L.A. Ivanov, The Euler-Poisson-Darboux equation in a Riemannian space. Soviet Math. Dokl. 24 (1981), 331–335.

    Google Scholar 

  21. Y. Kosman, Sur les degrées conformes des opérateurs differentiels, C.R. Acad. Sci. Paris. 280(1975), A 229–232.

    MathSciNet  Google Scholar 

  22. P.D. Lax and R.S. Phillips, An example of Huygens' principle. Comm. Pure Appl. Math. 31(1978), 415–423.

    Article  MathSciNet  MATH  Google Scholar 

  23. R.K. Sachs and H. Wu, General Relativity for Mathematicians. Springer Verlag, 1977.

    Google Scholar 

  24. R. Schimming, A review of Huygens' principle for linear hyperbolic differential equations. Proc. IMU Symposium, "Group Theoretical Methods in Mechanics" Novosibirsk, 1978.

    Google Scholar 

  25. J.A. Schouten, Über die konforme Abbildung n-dimensionaler Mannigfaltigkeiten mit quadratischer Massbestimmung auf eine Mannigfaltigkeit mit Euklidischer Massbestimmung. Math. Z. 11(1921), 58–88.

    Article  MathSciNet  MATH  Google Scholar 

  26. K. Stellmacher, Ein Beispiel einer Huygensschen Differentialgleichung. Gött. Nachr. 1953, 133–138.

    Google Scholar 

  27. O. Tedone, Sull'integrazionne dell'equazione ∂2Ф2/∂t2−∑i∂Ф/∂x 2i =0=0. Ann. di Mat. 3(1898), 1–24.

    Article  Google Scholar 

  28. H. Weyl, Reine Infinitesimalgeometrie.Math. Z. 2(1918), 384–411.

    Article  MathSciNet  MATH  Google Scholar 

  29. H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12(1960), 21–37.

    MathSciNet  MATH  Google Scholar 

  30. B. Ørsted, The conformal invariance of Huygens' principle. J. Differential Geometry 16(1981), 1–9.

    MathSciNet  MATH  Google Scholar 

  31. _____, Conformally invariant differential equations and projective geometry. J. Funct. Analysis. 44(1981), 1–23.

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. Sigurdur Helgason
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Rebecca Herb Raymond Johnson Ronald Lipsman Jonathan Rosenberg

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© 1984 Springer-Verlag

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Helgason, S. (1984). Wave equations on homogeneous spaces. In: Herb, R., Johnson, R., Lipsman, R., Rosenberg, J. (eds) Lie Group Representations III. Lecture Notes in Mathematics, vol 1077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072341

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  • DOI: https://doi.org/10.1007/BFb0072341

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13385-8

  • Online ISBN: 978-3-540-38936-1

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