# Laplace of F(ks)

1. May 6, 2014

### Jhenrique

1. The problem statement, all variables and given/known data
Compute the inverse laplace transform of F(ks)

2. Relevant equations

3. The attempt at a solution

$$L^{-1} (F(ks)) = \frac{f}{|k|} \left( \frac{t}{k} \right)$$

Correct?

2. May 6, 2014

### Staff: Mentor

Why do you think you need the absolute value of k?

What do you get from $\mathcal{L}(f(t/k))$, using the definition?

3. May 6, 2014

4. May 6, 2014

### xiavatar

You could just the fact that $\mathscr{F}[f](\lambda)=\frac{1}{\sqrt{2\pi}}\mathscr{L}[f](i\lambda)$ if we assume that $f(x)=0$ for $x<0$.

Where the Fourier Transform is the following $\mathscr{F}[f](\lambda)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f(x)e^{-ix\lambda}dx$

It should now be clearly what the inverse Laplace transform of the Fourier transform of a function is.

5. May 7, 2014

### Jhenrique

I did a simple question. I hoped a yes or not...

6. May 7, 2014

### xiavatar

Your answer is correct. Sorry about earlier, I mistook the F to be the Fourier transform.

7. May 8, 2014

### Jhenrique

Ok, thankyou!