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A problem of joint optimal bandwidth and power allocation in cognitive networks under fading channels is considered. It is assumed that multiple secondary users (SUs) share the spectrum of a primary user (PU) using frequency division multiple access. The bandwidth and power are allocated so as to maximize the sum ergodic capacity of all SUs under the total bandwidth constraint of the licensed spectrum as well as different combinations of the peak/average transmit power constraints at the SUs and the peak/average interference power constraint imposed by the PU. Although the optimization problem is convex, its dimension and, thus, complexity may be high. Therefore, computationally efficient ways of solving the problem are of importance and are investigated here by finding structures of the optimal solutions to the problem under different combinations of the constraints.