  We develop a framework to analyze the dynamics of a finite-dimensional
quantum system $\rm S$ in contact with a reservoir $\rm R$. The full,
interacting $\rm SR$ dynamics is unitary. The reservoir has a stationary state
but otherwise dissipative dynamics. We identify a main part of the full
dynamics, which approximates it for small values of the $\rm SR$ coupling
constant, uniformly for all times $t\ge 0$. The main part consists of explicit
oscillating and decaying parts. We show that the reduced system evolution is
Markovian for all times. The technical novelty is a detailed analysis of the
link between the dynamics and the spectral properties of the generator of the
$\rm SR$ dynamics, based on Mourre theory. We allow for $\rm SR$ interactions
with little regularity, meaning that the decay of the reservoir correlation
function only needs to be polynomial in time, improving on the previously
required exponential decay.
  In this work we distill the structural and technical ingredients causing the
characteristic features of oscillation and decay of the $\rm SR$ dynamics. In
the companion paper [27] we apply the formalism to the concrete case of an
$N$-level system linearly coupled to a spatially infinitely extended thermal
bath of non-interacting Bosons.
