Difference between revisions of "Bilateral Laplace transform"
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$$F(z,s)=\displaystyle\int_{-\infty}^{\infty} f(t)e_{\ominus z}(\sigma(t),s).$$ | $$F(z,s)=\displaystyle\int_{-\infty}^{\infty} f(t)e_{\ominus z}(\sigma(t),s).$$ | ||
This integral is clearly a generalization of the [[Laplace transform]]. | This integral is clearly a generalization of the [[Laplace transform]]. | ||
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| + | =References= | ||
| + | [http://marksmannet.com/RobertMarks/REPRINTS/2010-BilateralLaplaceTransformsOnTimeScales.pdf] | ||
Revision as of 01:41, 22 May 2015
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.
