What is the inverse laplace transform of this?

[Charles49]

$$F(s) = \frac{1}{K^s}$$

where K is a positive real.

 

[Count Iblis]

Hint:

Write this as exp[-s Log(k)]

Then compare this to the Laplace integral:

Integral of exp(-s t) f(t) dt

So, it looks like if you take f(t) to be a function that has a very large peak around t = Log(K), you'll get the correct Laplace transform up to some normalization. Now think of making this line of reasoning more precise...

 

[Charles49]

So is it $$\delta(t-\log(K))$$?

 

[Count Iblis]

So is it $$\delta(t-\log(K))$$?

That's right!