ABELIAN-TAUBERIAN THEOREM FOR LAPLACE-STIELTJES TRANSFORM OF HYPERFUNCTIONS
A. N. Deepthi and N. R. Mangalambal
Hyperfunctions are the generalized functions introduced by Mikio Sato in the late 1950’s. It can be considered as the analytic equivalent of distributions invented by Schwartz. Here we introduced the combined transform, Laplace-Stieltjes transform to hyperfunctions. Some properties of the combined transform is proved. Abelian – Tauberian theorem is also proved for this combined transform.
Keywords: Hyperfunctions, Laplace transform, Stieltjes transform.