No idea what this is saying...
The real part (or is it the magnitude of the complex f(t)) is less than Me^{yt}. Why is y any real number, and not restricted to say > 0.
Then 1.3, taking the laplace transform of the function derivative. Why is (s) outside? Shouldn't it be written L(f'(s))?
Fairly stumped at what this is trying to tell me
Write (1.3) as $L(f')(s) =sL(f)(s)-f(0) $.
Putting $f'$ for $f$, this becomes $L(f'')(s) =sL(f')(s)-f'(0) $.
Putting (1.3) in this, we get $L(f'')(s) =s(sL(f)(s)-f(0))-f'(0) =s^2L(f)(s)-sf(0)-f'(0) $.
By induction, we can get a formula for $L(f^{(n)})(s) $.