  In this work, we address the problem of optimal spectrum management in
continuous frequency domain in multiuser interference channels. The objective
is to maximize the weighted sum of user capacities. Our main results are as
follows: (i) For frequency-selective channels, we prove that in an optimal
solution, each user uses maximum power; this result also generalizes to the
cases where the objective is to maximize the weighted product (i.e.,
proportional fairness) of user capacities. (ii) For the special case of two
users in flat channels, we solve the problem optimally.
