  We describe a new method to estimate the trilinear period on automorphic
representations of PGL(2,R). Such a period gives rise to a special value of the
triple L-function. We prove a bound for the triple period which amounts to a
subconvexity bound for the corresponding special value. Our method is based on
the study of the analytic structure of the corresponding unique trilinear
functional on unitary representations of PGL(2,R).
