Abstract
The space of new generalized functions has been constructed. The operation of associative multiplication has been defined on this space. The Extended Laplace Transform has been defined
Highlights
If f (t) is defined for t ≥ 0, the improper ∞integral K (s,t) f (t)dt has many important applications
In algebra ζ (∏(R)) we define the associative multiplication for λ = + I *(∏(R)), γ = (γ k ) + I *(∏(R)) by ρk (F (z)) = sup F (i) (z) satisfy the inequality (2.1)
E, where E be separated locally -convex algebra with topology defined by family of semi norms (Pα )α∈A such that for α ∈ A, there exist β ∈ A a constant Cα > o for b
Summary
If f (t) is defined for t ≥ 0 , the improper ∞integral K (s,t) f (t)dt has many important applications. In [1] we defined the space ζ(E) as a factor space T *(E) / I *(E) [5] and we proved many Important results for this space. In algebras ξ (E) constructed in[1,2,3,4,5] all the operations of multiplication convolution, differentiation are defined.
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