We begin with a sequence M of positive real numbers and we consider the Denjoy-Carleman class C M . We show how to construct M-approximate solutions for complex vector fields with C M coefficients. We then use our construction to study micro-local properties of boundary values of approximate solutions in general M-involutive structures of codimension one, where the approximate solution is defined in a wedge whose edge (where the boundary value exists) is a maximally real submanifold. We also obtain a C M version of the Edge-of-the-Wedge Theorem.Published by Elsevier Inc.
In this paper, we use Borel's procedure to construct Gevrey approximate solutions of an initial value problem for involutive systems of Gevrey complex vector fields. As an application, we describe the Gevrey wave-front set of the boundary values of approximate solutions in wedges W of Gevrey involutive structures (M, V). We prove that the Gevrey wave-front set of the boundary value is contained in the polar of a certain cone Γ T (W) contained in V ∩ T X where X is a maximally real edge of W. We also prove a partial converse.
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