Quadratic Lie conformal superalgebras related to Novikov superalgebras

We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every Novikov superalgebra (V, circle), we construct an enveloping differential Poisson superalgebra U(V) with a derivation d such that u circle v= ud(v) and {u, v } = u circle v - (-1)(vertical bar u parallel to v vertical bar)v circle u for u, v is an element of V. The latter means that the commutator Gelfand-Dorfman superalgebra of V is special. Next, we prove that every quadratic Lie conformal superalgebra constructed on a finite-dimensional special Gelfand-Dorfman super(a)lgebra has a finite faithful conformal representation. This statement is a step towards a solution of the following open problem: whether a finite Lie conformal (super)algebra has a finite faithful conformal representation.