June 11th, 2017, 04:05 PM  #1 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित  Laplace transform kernel
What does "kernel of laplace transform is e^{st}" mean?

June 12th, 2017, 04:28 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 716 
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 
June 12th, 2017, 04:38 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
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. 
June 13th, 2017, 08:57 AM  #4 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित 
Thanks for clearing.


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kernel, laplace, transform 
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