An analytical/numerical approach, based on the Van Vleck Green function, was developed in order to analyze spectrally multiplexed beam combining of a linear array of fiber lasers, in which a blazed diffraction grating located in an external cavity plays the role of a spatially dispersive element. The focus is on the laser-external cavity coupling, which determines excess cavity loss, as affected by primary aberrations of the transform lens. Other issues are also touched upon, however, such as beam quality and bandwidth dependence on element location, and the optimization of the latter. Analytical results were supported by a more general numerical implementation. Typical values for bandwidth were found optimally as low as a few GHz, which, being substantially narrower than the free-running fiber laser line-width, maximum power limits are foreseeably determined by stimulated light scattering. A rough but encouraging degree of agreement of the resonator theory with independent lens aberration calculations and preliminary experiments performed at MIT/LL using triplet and quadruplet transform lenses was encountered so far.