Conormality, Cusps and Non-Linear Interaction

In this note we consider the problem of associating to a given geometry, in the form of a <Emphasis FontCategory=“NonProportional”>C</Emphasis>∞ variety containing possibly singular submanifolds, spaces of finitely regular conormal functions. For non-linear problems it is highly desirable that the bounded elements in these spaces form algebras and that they have appropriate solvability properties for certain linear differential operators. This leads to the general approach discussed here, mixing microlocalization and blow-up techniques.