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We review and extend the description of ultradifferentiable functions bytheir almost analytic extensions, i.e., extensions to the complex domain withspecific vanishing rate of the $\bar \partial$-derivative near the real domain.We work in a general uniform framework which comprises the main classicalultradifferentiable classes but also allows to treat unions and intersectionsof such. The second part of the paper is devoted to applications in microlocalanalysis. The ultradifferentiable wave front set is defined in this generalsetting and characterized in terms of almost analytic extensions and of the FBItransform. This allows to extend its definition to ultradifferentiablemanifolds. We also discuss ultradifferentiable versions of the ellipticregularity theorem and obtain a general quasianalytic Holmgren uniquenesstheorem.

Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis