Around Widder's characterization of the Laplace transform of an element of $L^{∞}(ℝ^{+})$
Jan Kisyński · Annales Polonici Mathematici · 2000
Let ϰ be a positive, continuous, submultiplicative function on $ℝ^{+}$ such that $lim_{t→∞} e^{-ωt}t^{-α}ϰ(t) = a$ for some ω ∈ ℝ, α ∈ $\overline{ℝ^{+}}$ and $a ∈ ℝ^{+}$. For every λ ∈ (ω,∞) let $ϕ_{λ}(t) =e^{-λt}$ for $t ∈ ℝ^{+}$. Let $L^{1}_{ϰ}(ℝ^{+})$