  We prove several multiplicity one theorems in this paper. For k a local field
not of characteristic two, and V a symplectic space over k, any irreducible
admissible representation of the symplectic similitude group GSp(V) decomposes
with multiplicity one when restricted to the symplectic group Sp(V). We prove
the analogous result for GO(V) and O(V), where V is an orthogonal space over k.
When k is non-archimedean, we prove the uniqueness of Fourier-Jacobi models for
representations of GSp(4), and the existence of such models for supercuspidal
representations of GSp(4).
