  We calculate the Overhauser frequency shifts in semiconductor nanostructures
resulting from the hyperfine interaction between nonequilibrium electronic
spins and nuclear spins. The frequency shifts depend on the electronic local
density of states and spin polarization as well as the electronic and nuclear
spin relaxation mechanisms. Unlike previous calculations, our method accounts
for the electron confinement in low dimensional semiconductor nanostructures,
resulting in both nuclear spin polarizations and Overhauser shifts that are
strongly dependent on position. Our results explain previously puzzling
measurements of Overhauser shifts in an Al$_x$Ga$_{1-x}$As parabolic quantum
well by showing the connection between the electron spin lifetime and the
frequency shifts.
