What is the proof of the following property? :

If F of class A and then :

Printable View

- December 31st 2010, 07:28 AMLiverpoolProving one of the laplace transform properties
What is the proof of the following property? :

If F of class A and then :

- December 31st 2010, 10:43 AMchisigma
Setting You have...

(1)

Integrating (1) You obtain...

(2)

Kind regards

- December 31st 2010, 01:10 PMKrizalid
another statement is if has limit as and is exponentially bounded, then

the proof is basically to write since is well defined for then use the Laplace transform for integrate between and use that the Laplace transform of a function tends to 0 as - December 31st 2010, 01:32 PMLiverpool
I did not get it ;|

Can you give me a full proof?

Am lost :/ - December 31st 2010, 02:09 PMDrexel28
- December 31st 2010, 02:15 PMLiverpool
- January 1st 2011, 12:42 PMchisigma
I apologize for the fact that a [stupid...] 'competition stress' often produces incomplete or 'impossible to undestand' answers(Thinking)...

Setting we have...

(1)

... and the first step is terminated. The (1) can be written as an ordinary first order DE as follows...

(2)

... with the 'condition' and its solution is...

(3)

Kind regards

- January 3rd 2011, 03:09 PMLiverpool
Thanks!

Now it is too clear :)