HELMHOLTZ OPERATORS AND SYMMETRICAL SPACE DUALITY

We consider the property of vanishing logarithmic term (VLT) for the f undamental solution of the shifted Laplace-d'Alembert operators square + b (b a constant), on pseudo-Riemannian reductive symmetric spaces M . Our main result is that such an operator on the c-dual or Flensted-J ensen dual of M has the VLT property if and only if a corresponding op erator on M does. For Lorentzian spaces, where the square + b are hype rbolic, VLT is known to be equivalent to the strong Huygens principle. We use our results to construct a large supply of new (space, operato r) pairs satisfying Huygens' principle.