Let G=ResE/FH, where H is a connected reductive group over a number field F and E/F is a quadratic extension. We define the regularized period of an automorphic form of G relative to H, and we express the regularized period of cuspidal Eisenstein series in terms of intertwining periods, which are relative analogues of the standard intertwining operators. This leads to an analogue of the Maass-Selberg relations. The regularized periods appear in the contribution of the continuous spectrum to the relative trace formula.
Erez M. Lapid. Jonathan D. Rogawski. "Periods of Eisenstein series: The Galois case." Duke Math. J. 120 (1) 153 - 226, 1 October 2003. https://doi.org/10.1215/S0012-7094-03-12016-5