By L. Boutet de Monvel (auth.), Anne Boutet de Monvel, Petre Dita, Gheorghe Nenciu, Radu Purice (eds.)
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Extra resources for Recent Developments in Quantum Mechanics: Proceedings of the Brasov Conference, Poiana Brasov 1989, Romania
The first assertion, relative to A, is just the usual existence theorem. The other cases are more delicate; one prove them by arguments close to the arguments used by Wasow [W] in the theory of asymptotic expansions. In the next sections, I will write ker(q,A) = A(q), ker(q,A';;;l) = A';;;\q), etc. 3) And others similar equalities (but these are the only ones that I will use). I will only explain here how one describes A<-l(q), A';;;l(q)/A<-l(q) , and A(q)/A';;;l(q) by Fourier transform. This is actually the elementary part of the business.
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Acad. Sci. N. Levy. Riemann-Roch theorem for complex spaces. Acta Math. 158 (1987) 149-188. Malgrange. L'involutivite des caracteristiques des systemes differentiels et microdifferentiels. Seminaire Bourbaki 1977-78, n0552. Malgrange. Sur les images directes de 49-71. Sjostrand. Fourier Integral operators with complex valued phase functions. Lecture Notes in Math. 459, Springer Verlag (1974) 120-223. Nguon. Modeles d'operateurs pseudodifferentiels ou de Toeplitz operant sur des espaces de fonctions de type exponentiel.