WeightedL p closure theorems for spaces of entire functions

For a fixed weight Δ(dx) onR ¹ and a linear space ℋ ⊆L ^p(Δ) of entire functions that is closed under difference quotientsh(·)→(z−·) ⁻¹[h(z)−h(·)], theL ^p(Δ) closure of ℋ is studied and characterized in terms of the normsL(z), (z∈C ¹ of the evaluation functionalsh→h(z),h∈ℋ. Partially supported by DA-ARO-31-124-71-6182 and NSF GP-43011.