On the continuous linear right inverse for convolution operators in spaces of ultradifferentiable functions

On solutions of convolution equations in spaces of ultradifferentiable functions

“…If γ is sufficiently small, the disks C s are mutually disjoint. Similar symbols μ that determine resolvable convolution equations in E 1 (ω) (I) were treated in [16].…”

Solvability of inhomogeneous Cauchy–Riemann equation in spaces of functions with a system of uniform weight estimates

“…In particular, it is used for solving of problems on generators in spaces of entire functions [2,3], problems on separation of singularities of holomorphic functions [3], interpolation problems [4], Borel-Whitney extension [5], in studies of convolution equations and ideals in various spaces [6,7], conjugated spaces [8,9] and so on.…”

“…In inductive spaces we have to satisfy only one estimate from a family, and the H¨ormander result is sufficient to this end. The H¨ormander theorem is applied in that way in the cited above papers [5][6][7][8][9].…”

“…Here H Φm (C) is continuously embedded into H Φ m+1 (C), m ∈ N. We consider the union of all these spaces H Φ (C) = Theorem 3 allow us, particularly, to obtain full description of symbols of the convolution operators in the Roumieu spaces of UDF. Let ω be a weight function in the sense of [7] (see also [5,14,15]); ϕ * ω (y) = sup{xy − ω(e x ) : x ≥ 0}, y ≥ 0, is Young conjugated to ω(e x ), ∞ > q n ↓ q ≥ 0, I = (−a, a) is finite or infinite interval in R, 0 < a m ↑ a.…”