A new proof to the period problems of GL(2)

We use the relations among the base change representations, theta lifts and Whittaker models, to give a new proof to the period problems of GL(2) over a quadratic local field extension E/F. We classify both local and global D×(F)-distinguished representations πD of D×(E), where D× is an inner form of GL(2) defined over a nonarchimedean field or a number field F.