Microlocal analysis in generalized function algebras based on generalized points and generalized directions

Abstract

We develop a refined theory of microlocal analysis in the algebra $\mathcal{G}(\Omega )$ of Colombeau generalized functions. In our approach, the wave front is a set of generalized points in the cotangent bundle of $\Omega$, whereas in the theory developed so far, it is a set of nongeneralized points. We also show consistency between both approaches.

10 pp; removed an erroneous claim in the Preliminaries section; otherwise identical to v1

References in corpus (2)

• Internal sets and internal functions in Colombeau theory
• Pointwise characterizations in generalized function algebras