Abstract
A calculus of polyhomogeneous paired Lagrangian distributions, associated to any two cleanly intersecting Lagrangain submanifolds, is constructed. The class is given an intrinsic characterisation using radial operators and a symbol calculus is developed. A class of pseudo—differential operators with singular symbols is developed within the calculus. This is used to give symbolic constructions of parametrices for operators of real principal type and paired Lagrangian distributions. The calculus is then applied to give a symbolic construction of the forward fundamental solution of the wave operator.
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