  We have obtained an expansion of the reduced density matrices (or,
equivalently, correlation functions of the fields) of impenetrable
one-dimensional anyons in terms of the reduced density matrices of fermions
using the mapping between anyon and fermion wavefunctions. This is the
generalization to anyonic statistics of the result obtained by A. Lenard for
bosons. In the case of impenetrable but otherwise free anyons with statistical
parameter $\kappa$, the anyonic reduced density matrices in the grand canonical
ensemble is expressed as Fredholm minors of the integral operator ($1-\gamma
\hat \theta_T$) with complex statistics-dependent coefficient $\gamma=(1+e^{\pm
i\pi\kappa})/ \pi$. For $\kappa=0$ we recover the bosonic case of Lenard
$\gamma=2/\pi$. Due to nonconservation of parity, the anyonic field correlators
$\la \fad(x')\fa(x)\ra$ are different depending on the sign of $x'-x$.
