  Rallis and Soudry have proven the stability under twists by highly ramified
characters of the local gamma factor arising from the doubling method, in the
case of a symplectic group or orthogonal group G over a local non-archimedean
field F of characteristic zero, and a representation of G, which is not
necessarily generic. This paper extends their arguments to show the stability
in the case when G is a unitary group over a quadratic extension E of F,
thereby completing the proof of the stability for classical groups. This
stability property is important in Cogdell, Piatetski-Shapiro, and Shahidi's
use of the converse theorem to prove the existence of a weak lift from
automorphic, cuspidal, generic representations of G(A) to automorphic
representations of GL(n,A) for appropriate n, to which references are given in
the paper of Rallis and Soudry.
