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We have obtained an expansion of the reduced density matrices (or,equivalently, correlation functions of the fields) of impenetrableone-dimensional anyons in terms of the reduced density matrices of fermionsusing the mapping between anyon and fermion wavefunctions. This is thegeneralization to anyonic statistics of the result obtained by A. Lenard forbosons. In the case of impenetrable but otherwise free anyons with statisticalparameter $\kappa$, the anyonic reduced density matrices in the grand canonicalensemble is expressed as Fredholm minors of the integral operator ($1-\gamma\hat \theta_T$) with complex statistics-dependent coefficient $\gamma=(1+e^{\pmi\pi\kappa})/ \pi$. 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 $x'-x$.

One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula