Theorems On nth Dimensional Laplace Transform
| Main Author: | Brigida, Michael; Physical Science Department Cavite State University |
|---|---|
| Format: | Article application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
JOURNAL OF INTERNATIONAL SCHOLARS’ CONFERENCE
, 2017
|
| Online Access: |
http://jurnal.unai.edu/index.php/JISC/article/view/307 |
Daftar Isi:
- 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 mappingLn : U→Vdefined by:Z ̃f( ̃sn) = L {F(x ̃n), ̃ F(x ̃n)e−( ̃sn·x ̃n)dx ̃n nRWhere F(x ̃n) ∈U and ̃sn ∈CnIn 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.