Global Wave-front Sets of Intersection and Union Type
We show that a temperate distribution belongs to an ordered intersection or union of admissible Banach or Fréchet spaces if and only if the corresponding global wave-front set of union or intersection type is empty. We also discuss the situation where intersections and unions of sequences of spaces with two indices are involved. A main situation where the present theory applies is given by sequences of weighted, general modulation spaces.
KeywordsWave-front Fourier Banach space modulation space micro-local pseudo-differential
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