Interpolation by entire functions with growth conditions

The Range of the Restriction Map for a Multiplicity Variety in Hörmander Algebras of Entire Functions

“…A 0 p (C)). Our results complement recent work by Ounaïes [18] and Massaneda, Ortega-Cerdà and Ounaïes [13].…”

“…2 We conclude this paper utilizing a reduction argument of Meise and Taylor [15] to obtain a consequence of the main result of [18] on the description of the range R V (A 0 p (C)) of the restriction operator on A 0 p (C) in terms of divided differences. To do this, let V = {(z k , m k )|k ∈ N} be a multiplicity variety and let p be a weight.…”

“…The arguments of Berenstein and Li [3] were simplified by Hartmann and Massaneda [11] and by Ounaïes [17] using Hörmander's L 2 estimates for the ∂ equation, treating also weights that are radial but not doubling. In [18] Ounaïes uses divided differences to characterize those sequences that are in the range R V (A p (C)) of the restriction map R V when the multiplicity variety satisfies the assumption (a) (i) in Theorem 1.1. This work was continued later by her jointly with Massaneda and Ortega-Cerdà in [13].…”

“…Given a sequence W := (w k,l ) k∈N,0≤l<m k of complex numbers, we denote by Φ(W ) := (ϕ k,l ) k∈N,0≤l<m k the divided differences of W defined by induction as in [18]. We denote bỹ A 0 p (V ) the set of all the sequences W := (w k,l ) k∈N,0≤l<m k such that their divided differences Φ(W ) := (ϕ k,l ) k∈N,0≤l<m k satisfy that for all ε > 0 there is A ε > 0 such that for all n ∈ N and all |z k | ≤ 2 n and 0 ≤ l < m k we have δ k,l := |ϕ k,l |2 n(l+m 1 +...+m k−1 ) ≤ A ε exp(εp(2 n )).…”

Geometric characterization of interpolation in the space of Fourier–Laplace transforms of ultradistributions of Roumieu type

“…For radial weights Berenstein, Li and Vidras [5] described interpolating varieties for entire functions of minimal type A 0 p . Compare also [25] and references therein. A special role is played by non-radial weights p(z) =|Im z| + ω(|z|).…”