We introduce global wave-front sets WF_{M(ω,B)}(f), f ∈ S ′(R^d), with respect to the modulation spaces M(ω, B), where ω is an appropriate weight function and 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(ω,B)}(f). In particular, we prove that microlocality and microellipticity hold for a class of globally defined pseudo-differential operators Op(a).
Global wave-front sets of Banach, Fréchet and Modulation space types, and pseudo-differential operators
CORIASCO, Sandro;
2013-01-01
Abstract
We introduce global wave-front sets WF_{M(ω,B)}(f), f ∈ S ′(R^d), with respect to the modulation spaces M(ω, B), where ω is an appropriate weight function and 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(ω,B)}(f). In particular, we prove that microlocality and microellipticity hold for a class of globally defined pseudo-differential operators Op(a).
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