-ultradistributions

By A V Abanin. 2008

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Pseudodifferential operators of infinite order in spaces of tempered ultradistributions (2013, methodology): “6 of [9], for arbitrary m′ > 0, we obtain eM(m|x ′|) ≤ eM(3mRm|β|)eM(8sm′Rm|β|)e−M(m′|(x,y)|) ≤ c0e ′)HRm|β|)e−M(m ′|(x,y)|), when (x, y) ∈ R\Ωr and χ|β|((1−τ)x+τy, ξ) 6= 0.”
Composition in ultradifferentiable classes (2012, background): “It is well-known that E [M ] is stable under composition, if M is log-convex, see [34], [20], [13], and usually in the literature log-convexity is assumed in order to have stability under composition; but is log-convexity also necessary? Actually, when proving stability under composition with Faá di”
Ultradistributions and Time-Frequency Analysis (2006, methodology): “Denjoy-Carleman-Komatsu [30], BeurlingBjörck [3], Braun-Meise-Taylor [4], Cioranescu-Zsidó [10].”
The convenient setting for non-quasianalytic Denjoy–Carleman differentiable mappings☆ (2008, methodology): “Or we may work with Whitney jets on compact K , like [13].”
Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces (2012, background): “We refer to [5] for the extensive analysis of these spaces and their duals in R.”