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Maslov indices on the metaplectic group M p ( n )

Maurice De Gosson — 1990

Annales de l'institut Fourier

We use the properties of M p ( n ) to construct functions μ : M p ( n ) Z 8 associated with the elements of the lagrangian grassmannian Λ (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between M p ( n ) and a subset of S p ( n ) × Z 8 , equipped with appropriate algebraic and topological structures.

Microlocal regularity at the boundary for pseudo-differential operators with the transmission property (I)

Maurice De Gosson — 1982

Annales de l'institut Fourier

This work is devoted to a systematic study of the microlocal regularity properties of pseudo-differential operators with the transmission property. We introduce a “boundary singular spectrum”, denoted W F ω ( u ) for distributions u D ' ( R + n ) , regular in the normal variable x n (thus, W F ω ( u ) = means that u s + t = 1 / 2 H s + t near the boundary), and it is shown that W F ω - m [ P ( u 0 ) x n > 0 ] is a subset of W F ( u ) if P has degree m and the transmission property. We finally prove that these results can bef used to examinate the (microlocal) regularity of the solutions of differential...

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