Contents
Property 1
ROC of the Laplace Transform consists of vertical strips in the complex plane (could be empty or could be entire plane).
Why is this
ROC of $ X(s) $ consists of those $ s = a + j\omega $ for which the Fourier Transform of $ x(t)e^{-at} $ converges.
This Condition only depends on $ a = Re(s) $.
Property 2
If $ x(t) $ is of "finite duration" and if $ \int_{-\infty}^{\infty} |x(t)| dt $ is finite,
Then $ \int_{-\infty}^{\infty} x(t)e^{-st} dt $ converges for all values of s.
Sources
Properties come from Mimi's Lecture #30.
