Given an LTI analog system whose impulse response is $h(t)$, its transfer function is $$H(s)=L[h(t)]$$ Where L indicates the Laplace transform. It turns out that the zero-state response $y(t)$ of the system to the input signal $x(t)$ can be easily obtained in the s-domain by the formula: $$Y(s) = H(s) X(s)$$ where uppercase letters indicate the Laplace transform of the signals involved.