  We revisit the model of a quantum Brownian oscillator linearly coupled to an
environment of quantum oscillators at finite temperature. By introducing a
compact and particularly well-suited formulation, we give a rather quick and
direct derivation of the master equation and its solutions for general spectral
functions and arbitrary temperatures. The flexibility of our approach allows
for an immediate generalization to cases with an external force and with an
arbitrary number of Brownian oscillators. More importantly, we point out an
important mathematical subtlety concerning boundary-value problems for
integro-differential equations which led to incorrect master equation
coefficients and impacts on the description of nonlocal dissipation effects in
all earlier derivations. Furthermore, we provide explicit, exact analytical
results for the master equation coefficients and its solutions in a wide
variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with
a finite cut-off.
