Global Wave Front Set of Modulation Space types

Details Global Wave Front Set of Modulation Space types Global Wave Front Set of Modulation Space types

2009-12-17

arxiv.org/abs/0912.3366v1

Mathematics

Functional Analysis

Pre-version, 29 pages

Scientific paper

We introduce global wave-front sets ${WF}_{M(\omega,\mathscr B)}(f)$, $f\in {\mathscr S}^\prime(\mathbf{R}^d)$, with respect to the modulation spaces $M(\omega,\mathscr B)$, where $\omega$ is an appropriate weight function and $\mathscr B$ is a translation invariant Banach function space. We show that the standard properties for known notions of wave-front set extend to ${WF}_{M(\omega,\mathscr B)}(f)$. In particular, we prove that microlocality and microellipticity hold for a class of globally defined pseudo-differential operators.

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