  For the group G = PGL(2) we prove nonstandard matching and the fundamental
lemma between two relative trace formulas: on one hand, the relative trace
formula of Jacquet for the quotient T\G/T, where T is a nontrivial torus; on
the other, the Kuznetsov trace formula with nonstandard test functions. The
matching is nonstandard in the sense that orbital integrals are related to each
other not one-by-one, but via an explicit integral transform. These results
will be used in the sequel to compare the corresponding global trace formulas
and reprove the celebrated result of Waldspurger on toric periods.
