Search for D^0 - barD^0 Mixing in the Dalitz Plot Analysis of D^0 --> K_S^0 pi^+ pi^-

The resonant substructure in D0 -> K0Spi+pi- decays is described by a combination of ten quasi two-body intermediate states which include both CP-even and CP-odd eigenstates and one doubly-Cabibbo suppressed channel. We present a formalism that connects the variation in D0 decay time over the Dalitz plot with the mixing amplitudes, x and y, that describe off-shell and on-shell D0-D0B mixing. We analyze the CLEO II.V data sample and find the amplitudes x and y are consistent with zero. We limit $(-4.5 < x < 9.3)%$ and (-6.4< y < 3.6)%$ at the 95% confidence level.