Title

Helmholtz operators and symmetric space duality

Document Type

Article

Publication Date

1-1-1997

Abstract

We consider the property of vanishing logarithmic term (VLT) for the fundamental solution of the shifted Laplace-d'Alembert operators □ + 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-Jensen dual of M has the VLT property if and only if a corresponding operator on M does. For Lorentzian spaces, where the □ + b are hyperbolic, VLT is known to be equivalent to the strong Huygens principle. We use our results to construct a large supply of new (space, operator) pairs satisfying Huygens' principle.

Publication Source (Journal or Book title)

Inventiones Mathematicae

First Page

63

Last Page

74

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