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Lagrangian intersection and the Cauchy problem. (English) Zbl 0396.58006
A symbolic calculus for distributions associated to a pair of Lagrangian manifolds intersecting cleanly with codimension one is developed and applied to give a purely symbolic construction of global parametrices for pseudodifferential operators of real principal type on a pseudoconvex manifold. A calculus of distributions associated to a more complicated arrangement of Lagrangians is used to get global parametrices for pseudodifferential operators with double involutive characteristics under the Levi condition. The Cauchy problem for weakly hyperbolic operators of this type is solved using such parametrices.
Reviewer: R. B. Melrose

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
58J45 Hyperbolic equations on manifolds
35S05 Pseudodifferential operators as generalizations of partial differential operators
47G30 Pseudodifferential operators
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