  We consider the supercircle $S^{1|1}$ equipped with the standard contact
structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie
superalgebra of contact vector fields; it contains the M\"obius superalgebra
$osp(1|2)$. We study the space of linear differential operators on weighted
densities as a module over $osp(1|2)$. We introduce the canonical isomorphism
between this space and the corresponding space of symbols and find interesting
resonant cases where such an isomorphism does not exist.
