Factorization in Denjoy-Carleman classes associated to representations of (Rd,+)

Abstract

For two types of moderate growth representations of (R d , +) on sequentially complete locally convex Hausdorff spaces (including F-representations [14]), we introduce Denjoy-Carleman classes of ultradifferentiable vectors and show a strong factorization theorem of Dixmier-Malliavin type for them. In particular, our factorization theorem solves [14, Conjecture 6.4] for analytic vectors of representations of G = (R d , +). As an application, we show that various convolution algebras and modules of ultradifferentiable functions satisfy the strong factorization property.

Projective descriptions of spaces of functions and distributions

“…4. A similar result to Proposition 4.1, (ii) in the setting of ultradistributions has been given in Section 7 of [13].…”

Projective descriptions of spaces of functions and distributions

“…4. A similar result to Proposition 6, (ii) in the setting of ultradistributions has been given in Section 7 of [12].…”

On extremal domains and codomains for convolution of distributions and fractional calculus

“…Proof It is known that every finite Φ ⊆ D is contained in acx(Ψ * Ψ ) for some other finite Ψ ⊆ D [14]. An examination of the proof in [14] reveals, that every Φ ∈ B(D) is contained in acx(Ψ * Θ) for some Ψ ∈ B(D) and some finite Θ ⊆ D (see also [12], where this is further generalized). Using this, one estimates…”