  For a finite field extension $F/\mathbb{Q}_p$ we associate a coefficient
system attached on the Bruhat-Tits tree of $G:= {\rm GL}_2(F)$ to a locally
analytic representation $V$ of $G$. This is done in analogy to the work of
Schneider and Stuhler for smooth representations. This coefficient system
furnishes a chain-complex which is shown, in the case of locally analytic
principal series representations $V$, to be a resolution of $V$.
