ITERATED STIELTJES TRANSFORM OF GENERALIZED FUNCTIONS

L. S. Dube

《International Journal of Mathematics and Mathematical Sciences》 1985卷 (1985/12) Pp. 425-432

https://doi.org/10.1155/S0161171285000461

並列摘要

The generalized S_2-transform of a member of f of a certain space of generalized functions is defined as F(x) = ＜f(t), K(x, t; ρ)＞, where K(x, t; ρ) = ʃ_0^∞1/(x+y)^ρ(y+t)^ ρ dy, ρ ＞ 1/2, o ＜ x ＜ ∞ and o ＜ t ＜ ∞ An inversion theorem for the transform is established interpreting the convergence in the weak distributional sense.

並列關鍵字

Testing Function space ； Dual space ； Frechet space ； Iterated Stieltjes Transform ； Schwartz Distributions ； Generalized Functions