The Transforms of Fourier, the Transform of Laplas,the New For- Mula of Transformation

Abstract

A new inverse formula for the Laplas's transformation. Pavlov An.V.(MIREA(TU)). In the article is proved,that the complex part of the analytical continuation of the r(p) = LLZ(x) = ∞ 0 e −pt dt ∞ 0 e −tx Z(x)dx, p ∈ {p : Im p ≥ 0}, equals to −πZ(x), x ∈ (0, ∞), if p = s = −x ∈ (−∞, 0) for a wide class of a functions Z(x) : It is proved,that the odd functions Z(x) = l k=1 γ k e λ k x , γ k = res p=λ k Q n (p) Introduction. In the article we prove (a theorem 2),that for the negative variable p = −x, x ∈ (0, ∞) a complex part of the analytical continuation r(p) = LLZ(x) equals to −πZ(x), x ∈ (0, ∞) for a wide class of a functions Z(x) :