In this talk I will describe a semi-classical analog of the classical theory of Hermite distributions developed by Boutet de Monvel and Guillemin about 40 years. More precisely, to each isotropic submanifold of the phase space, we define a space of semi-classical wave functions which can be viewed as a quantization of the isotropic submanifold, and we develop the corresponding symbol theory. I will also discuss a couple applications of the theory. This is a joint work with Alejandro Uribe and Victor Guillemin.

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