Differential Operators on Supercircle: Conformally Equivariant Quantization and Symbol Calculus

We consider the supercircle S1|1 equipped with the standard contact structure. The Lie superalgebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{K}(1)}$$\end{document} 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.