  We use the uniqueness of various invariant functionals on irreducible unitary
representations of PGL(2,R) in order to deduce the classical Rankin-Selberg
identity for the sum of Fourier coefficients of Maass cusp forms and its new
anisotropic analog. We deduce from these formulas non-trivial bounds for the
corresponding unipotent and spherical Fourier coefficients of Maass forms. As
an application we obtain a subconvexity bound for certain L-functions. Our main
tool is the notion of Gelfand pair.
