Differential operators on supercircle: Conformally equivariant quantization and symbol calculus

We consider the supercircle S 1|1 equipped with the standard contact structure. The Lie superalgebra Script K Sing(1) of contact vector fields contains the Möbius 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 all cases where such an isomorphism does not exist. © Springer 2007.