Difference between revisions of "Bilateral Laplace transform"

From timescalewiki
Jump to: navigation, search
(One intermediate revision by the same user not shown)
Line 4: Line 4:
*{{PaperReference|Bilateral Laplace Transforms on Time Scales: Convergence, Convolution, and the Characterization of Stationary Stochastic Time Series|2009|John M. Davis|author2=Ian A. Gravagne|author3=Robert J. Marks II|prev=findme|next=findme}}: $(3.1)$

Latest revision as of 17:34, 7 July 2017

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 $$F(z,s)=\displaystyle\int_{-\infty}^{\infty} f(t)e_{\ominus z}(\sigma(t),s) \Delta t.$$ This integral is clearly a generalization of the Laplace transform.