Search for D⁰ - barD⁰ Mixing in the Dalitz Plot Analysis of D⁰ --> K_S⁰ pi^+ pi^-

The resonant substructure in D0 --> K0S pi+ 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 parameters, x and y, that describe off-shell and on-shell D0-D0B mixing. We analyze the CLEO II.V data sample and find the parameters x and y are consistent with zero. We limit (-4.7 < x < 8.6)% and (-6.1 < y < 3.5)% at the 95\% confidence level