  We present a theoretical approach to calculate the {\it local} absorption
spectrum of excitons confined in a semiconductor nanostructure. Using the
density-matrix formalism, we derive a microscopic expression for the non-local
susceptibility, both in the linear and non-linear regimes, which includes a
three-dimensional description of electronic quantum states and their Coulomb
interaction. The knowledge of the non-local susceptibility allows us to
calculate a properly defined local absorbed power, that depends on the
electro-magnetic field distribution. We report on explicit calculations of the
local linear response of excitons confined in single and coupled T-shaped
quantum wires with realistic geometry and composition. We show that significant
interference effects in the interacting electron-hole wavefunction induce new
features in the space-resolved optical spectra, particularly in coupled
nanostructures. When the spatial extension of the electromagnetic field is
comparable to the exciton Bohr radius, Coulomb effects on the local spectra
must be taken into account for a correct assignment of the observed features.
