Huygens’ principle and hadamard’s conjecture

@article{Gnther1991HuygensPA,
  title={Huygens’ principle and hadamard’s conjecture},
  author={P. A. G{\"u}nther},
  journal={The Mathematical Intelligencer},
  year={1991},
  volume={13},
  pages={56-63}
}
  • P. Günther
  • Published 1 March 1991
  • Mathematics
  • The Mathematical Intelligencer
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References

SHOWING 1-10 OF 20 REFERENCES
An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times
It is shown that the validity of Huygens'principle for the non-self-adjoint wave equation on a general Petrov type N space-time implies that the equation is equivalent to the conformally invariantExpand
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times
It is shown that the validity of Huygens' principle for the conformally invariant scalar wave equation, Maxwell's equations or Weyl's neutrino equation on a Petrov type III space-time, implies thatExpand
Le Tour De Monde En 80 Jours
« Phileas Fogg, en quittant Londres, ne se doutait guere, sans doute, du grand retentissement qu'allait provoquer son depart. Ce tour du monde a accomplir, autrement qu'en theorie et sur le papier,Expand
Zur Gültigkeit des Huygensschen Prinzips bei einer speziellen Metrik
In Anlehnung an die Arbeiten von Gunther [2], [3], wird die folgende Metrik betrachtet: ds2 = 2 dx1 dx2 - aIJ(x1) dxI dxJ, I, J = 3, 4, …, n, mit positiv definiter Matrix a = (aIJ). Es wird die FrageExpand
An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle †
The validity of Huygens' principle in the sense of Hadamard's ‘minor premise’ is investigated for scalar wave equations on curved space-time. A new necessary condition for its validity in emptyExpand
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