  We introduce a rigorous approach to the many-body spectral theory of extended
anyons, i.e. quantum particles confined to two dimensions that interact via
attached magnetic fluxes of finite extent. Our main results are many-body
magnetic Hardy inequalities and local exclusion principles for these particles,
leading to estimates for the ground-state energy of the anyon gas over the full
range of the parameters. This brings out further non-trivial aspects in the
dependence on the anyonic statistics parameter, and also gives improvements in
the ideal (non-extended) case.
