Question on Laplace Transform

x(t) = sin(t/2)
H(ω) = ∏(ω-0.5)
Find theoutput signal y(t)

I am able to use euler formula to get x(t) =(ei(0.5)t - eit(-0.5)) /2
However, H(w) = ∏(ω-0.5) is not found in the laplace transform truth table.

Can you help?