  Integrable quantum field theories in 1+1 dimensions have recently become
amenable to a rigorous construction, but many questions about the structure of
their local observables remain open. Our goal is to characterize these local
observables in terms of their expansion coefficients in a series expansion by
interacting annihilators and creators, similar to form factors. We establish a
rigorous one-to-one characterization, where locality of an observable is
reflected in analyticity properties of its expansion coefficients; this
includes detailed information about the high-energy behaviour of the observable
and the growth properties of the analytic functions. Our results hold for
generic observables, not only smeared pointlike fields, and the characterizing
conditions depend only on the localization region - we consider wedges and
double cones - and on the permissible high energy behaviour.
