The Quasiasymptotic Expansion at the Origin. Abelian-Type Results for Laplace and Stieltjes Transforms

The notion of quasiasymptotic expansion at the origin of tempered distributions supported by 0, α] and the structural theorem for such distributions that have the quasiasymptotic expansion at the origin are given. As applications, the Abelian-type results for the distributional Stieltjes and Laplace transforms are obtained.