All Questions

Of all the examples I know of (bilateral) Laplace transforms $F$ defined on their maximal vertical strips $V_{a,b}=\{ z \in \mathbf{C} : a < \operatorname{Re}(z) < b \}$ with $-\infty < a <...

Let $f:[0,\infty)\to \mathbb{R}$ be a piecewise differentiable function with $f(0)=0$ and $f'(t)$ of bounded variation. Its Laplace transform $\mathcal{L}f$ converges for $\Re s > 0$. Assume it can ...

If I have a function and I want to represent it as being the Laplace transform of another, that is, I want to be sure that there is $\hat{f}(s)$ such that my function $f(x)$ can be written as: $$f(x) =...

In solving a linear system, when would I use a Fourier transform versus a Laplace transform? I am not a mathematician, so the little intuition I have tells me that it could be related to the boundary ...

My question is whether we can extract information about how fast an integrable function converges to zero by looking at the asymptotics of its Laplace transform. More concrete case, let $f:\mathbb{R} ...