Helmholtz operators and symmetric space duality |
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Authors: | Thomas Branson Gestur Ólafsson |
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Institution: | (1) Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA (branson@math.uiowa.edu), US;(2) Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA (olafsson@marais.math.lsu.edu), US |
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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.
Oblatum 23-XII-1995 & 22-VIII-1996 |
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