Acta Mathematica

Helmholtz operators on harmonic manifolds

Rainer Schimming and Henrik Schlichtkrull

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Article information

Source
Acta Math. Volume 173, Number 2 (1994), 235-258.

Dates
Received: 21 December 1992
Revised: 2 December 1993
First available in Project Euclid: 31 January 2017

Permanent link to this document
http://projecteuclid.org/euclid.acta/1485890816

Digital Object Identifier
doi:10.1007/BF02398435

Zentralblatt MATH identifier
0818.58042

Rights
1994 © Almqvist & Wiksell

Citation

Schimming, Rainer; Schlichtkrull, Henrik. Helmholtz operators on harmonic manifolds. Acta Math. 173 (1994), no. 2, 235--258. doi:10.1007/BF02398435. http://projecteuclid.org/euclid.acta/1485890816.


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References

  • Berger, M., Gauduchon, P. & Mazet, E., Le spectre d'une variété Riemannienne. Lecture Notes in Math., 194. Springer-Verlag, Berlin-New York, 1971.
  • Besse, A. L., Manifolds all of whose Geodesics are Closed. Springer-Verlag, Berlin-New York, 1978.
  • —, Einstein Manifolds. Springer-Verlag, Berlin-New York, 1987.
  • Damek, E. & Ricci, F., A class of non-symmetric harmonic Riemannian spaces. Bull. Amer. Math. Soc., 27 (1992), 139–142.
  • Erdelyi, A. et al., Higher Transcendental Functions, Vol. 1. McGraw-Hill, New York, 1953.
  • Faraut, J., Distributions sphériques sur les espaces hyperboliques. J. Math. Pures Appl. (9), 58 (1979), 369–444.
  • Günther, P., Huygens' Principle and Hyperbolic Equations. Academic Press, San Diego, Calif., 1988.
  • Hadamard, J., Lectures on Cauchy's Problem in Linear Partial Differential Equations. Yale Univ. Press, New Haven, Conn., 1923.
  • Helgason, S., Differential operators on homogeneous spaces. Acta Math., 102 (1959), 239–299.
  • —, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassman manifolds. Acta Math., 113 (1965), 153–180.
  • —, Differential Geometry, Lie Groups and Symmetric Spaces. Academic Press, New York, 1978.
  • —, Groups and Geometric Analysis. Academic Press, Orlando, Fla, 1984.
  • —, Wave Equations on Homogeneous Spaces. Lecture Notes in Math., 1077, pp. 254–287. Springer-Verlag, Berlin-New York, 1984.
  • Kolk, J. & Varadarajan, V. S., Lorentz invariant distributions supported on the forward light cone. Compositio Math., 81 (1992), 61–106.
  • Mostepanenko, V. M. & Sokolov, I. Yu., New restrictions on the parameters of the spin-1 antigravitation. Phys. Lett. A, 132 (1988), 313–315.
  • Orloff, J., Orbital integrals on symmetric spaces, in Non-Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Math., 1243, pp. 198–239. Springer-Verlag, Berlin-New York, 1987.
  • Ørsted, B., The conformal invariance of Huygens' principle. J. Differential Geom., 16 (1981), 1–9.
  • —, Conformally invariant differential equations and projective geometry. J. Funct. Anal., 44 (1981), 1–23.
  • Recami, E. & Tonin-Zanchin, V., Fifth force, sixth force and all that. Nuovo Cimento B, 105 (1990), 701–705.
  • Riesz, M., L'intégrale de Riemann-Liouville et le problème de Cauchy. Acta Math., 81 (1949), 1–223.
  • Ruse, H. S., Walter, A. G. & Willmore, T. J., Harmonic Spaces. Edizioni Cremonese, Rome, 1961.
  • Schimming, R., Laplace-like linear differential operators with a logarithm-free elementary solution. Math. Nachr., 148 (1990), 145–174.
  • —, Harmonic differential operators. Forum Math., 3 (1991), 177–203.
  • Schimming, R., Hadamard analysis of products of Laplace-like differential operators. In preparation.
  • Schwartz, L., Theorie des distributions I. Hermann, Paris, 1957.
  • Stellmacher, K. L., Ein Beispiel einer Huygensschen Differentialgleichung. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 10 (1953), 133–138.
  • Szabó, Z. I., The Lichnerowicz conjecture on harmonic manifolds. J. Differential Geom., 31 (1990), 1–28.
  • Takahashi, R., Quelques résultats sur l'analyse harmonique dans l'espace symétrique non compact de rang 1 du type exceptionnel, in Analyse harmonique sur les groupes de Lie II. Lecture Notes in Math., 739, pp. 511–567. Springer-Verlag, Berlin-New York, 1979.
  • Wolf, J., Spaces of Constant Curvature. McGraw-Hill, New York, 1967.