  The equivalence of the anti-selfduality Yang-Mills equations on the
4-dimensional orientable Riemannian manifold and Laplace equations for some
infinite dimensional Laplacians is proved. A class of modificated Levy
Laplacians parameterized by the choice of a curve in the group $SO(4)$ is
introduced. It is shown that a connection is an instanton (a solution of the
anti-selfduality Yang-Mills equations) if and only if the parallel transport
generalized by this connection is a solution of the Laplace equations for some
three modificated Levy Laplacians from this class.
