  We derive an exact operator bosonization of a finite number of fermions in
one space dimension. The fermions can be interacting or noninteracting and can
have an arbitrary hamiltonian, as long as there is a countable basis of states
in the Hilbert space. In the bosonized theory the finiteness of the number of
fermions appears as an ultraviolet cut-off. We discuss implications of this for
the bosonized theory. We also discuss applications of our bosonization to
one-dimensional fermion systems dual to (sectors of) string theory such as LLM
geometries and c=1 matrix model.
