Theorems On nth Dimensional Laplace Transform - Brigida, Michael (Journal of International Scholars Conference - EDUCATION/SOCIAL SCIENCES, 2016)
Let U be the set of all functions from [0,∞)n to R and V be the set of all functions from S ⊆Cn to C.Then the nth dimensional Laplace transform is the mapping Ln : U→V defined by: Z˜ f(˜sn) = L F(x˜n),˜ F(x˜n)e−(˜sn·x˜n)dx˜n n R Where F(x˜n) ∈U and ˜sn ∈Cn In this paper we gave alternative proof for some theorems on properties of nth dimensional Laplace Transform, we proved that if F(x˜n) is piecewise continuous on [0,∞)n and function of exponential order ˜γn = (γ1,γ2,...,γn) then the nth dimensional Laplace Transform defined above exists, absolutely and uniformly convergent, analytic and infinitely differentiable on Re(s1) > γ1,Re(s2) > γ2,...,Re(s) > γn, and we gave also some corollaries of these results.