I have encountered a system where the output $y(t)$ and input $x(t)$ are related in the laplace domain as:
$$Y(s) = H(s)X(s) \tag1$$
which is typical. However, $H(s)$ is not a rational function of polynomials of $s$. Instead, $H(s)$ contains terms like $\log(s)$.
As far I knew, one can write equation $(1)$ only for an LTI system and LTI systems have rational polynomial transfer functions. Am I correct in this analysis?
If I have a logarithm in $H(s)$, that implies that I cannot write a linear differential equation with constant coefficients in the time domain. Is it possible to have an LTI system that is not representable by such differential equation?
Does a frequency domain analysis always imply an LTI system?