Bilateral Laplace transform
From timescalewiki
Revision as of 01:40, 22 May 2015 by Tom (talk | contribs) (Created page with "Let $\mathbb{T}$ be a time scale. The Bilateral Laplace transform of a function $f \colon \mathbb{T} \rightarrow \mathbb{T}$ centered at $s$ is given by $$F(z,s)=\displays...")
Let $\mathbb{T}$ be a time scale. The Bilateral Laplace transform of a function $f \colon \mathbb{T} \rightarrow \mathbb{T}$ centered at $s$ is given by $$F(z,s)=\displaystyle\int_{-\infty}^{\infty} f(t)e_{\ominus z}(\sigma(t),s).$$ This integral is clearly a generalization of the Laplace transform.
