  We consider the initial boundary value (IBV) problem for the focusing
nonlinear Schr\"odinger equation in the quarter plane $x>0,t>0$ in the case of
periodic initial data (at $t=0$) and a Robin boundary condition at $x=0$. Our
approach is based on the simultaneous spectral analysis of the Lax pair
equations combined with symmetry considerations for the corresponding
Riemann-Hilbert problems. A connection between the original IBV problem and an
associated initial value (IV) problem is established.
