Difference between revisions of "Covolution theorem for unilateral Laplace transform"
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$\ | + | $$\mathscr{L}_{\mathbb{T}}\{f*g\}(z)=\mathscr{L}\{f\}(z) \mathscr{L}\{g\}(z),$$ |
| − | where $\ | + | where $\mathscr{L}$ denotes the [[unilateral Laplace transform]] and $f*g$ denotes the [[unilateral convolution]]. |
==Proof== | ==Proof== | ||
Latest revision as of 13:44, 20 January 2023
Theorem
The following formula holds: $$\mathscr{L}_{\mathbb{T}}\{f*g\}(z)=\mathscr{L}\{f\}(z) \mathscr{L}\{g\}(z),$$ where $\mathscr{L}$ denotes the unilateral Laplace transform and $f*g$ denotes the unilateral convolution.
