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June 11th, 2017, 04:05 PM   #1
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Laplace transform kernel

What does "kernel of laplace transform is e^{-st}" mean?
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June 12th, 2017, 04:28 PM   #2
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Laplace transform is defined as an integral of the product of the kernel and the function of interest.

https://en.wikipedia.org/wiki/Laplace_transform
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June 12th, 2017, 04:38 PM   #3
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The "kernel" of the integral transform $\displaystyle \int K(x, t) f(t)dt$ is, by definition, $K(x, t)$.

The Laplace transform is, as mathman showed, $\displaystyle \int_0^\infty e^{-st}f(t)dt$.

Last edited by skipjack; June 12th, 2017 at 10:19 PM.
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June 13th, 2017, 08:57 AM   #4
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Thanks for clearing.
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