  We prove that the double layer potential operator and the gradient of the
single layer potential operator are L_2 bounded for general second order
divergence form systems. As compared to earlier results, our proof shows that
the bounds for the layer potentials are independent of well posedness for the
Dirichlet problem and of De Giorgi-Nash local estimates. The layer potential
operators are shown to depend holomorphically on the coefficient matrix A\in
L_\infty, showing uniqueness of the extension of the operators beyond singular
integrals. More precisely, we use functional calculus of differential operators
with non-smooth coefficients to represent the layer potential operators as
bounded Hilbert space operators. In the presence of Moser local bounds, in
particular for real scalar equations and systems that are small perturbations
of real scalar equations, these operators are shown to be the usual singular
integrals. Our proof gives a new construction of fundamental solutions to
divergence form systems, valid also in dimension 2.
