space), Therefore a system of convolution equations arises for the unknown function g and functions h$_{k}$, where h$_{k}$ ( x ) = x$_{k}$g ( x ) , Another model that leads to a system of equations is nonparametric re- gression with Berkson error (see, e.g. Meister, 2009 for review). Consider a nonparametric regression model E ( w ( z ) x$_{k}$ | z ) = E ( w ( z ) x ∗ $_{k}$| z ) = ∫ ( z$_{k}$ − u$_{k}$ ) g ( z − u ) f ( u ) du. g ∗ f = w$_{1}$ ; ( h$_{k}$ ) ∗ f = w$_{2}$$_{k}$, k = 1 , ...d. (3) y = g ( x ) + u$_{y}$, z = x + u, (4) where x may be correlated with the error, u$_{y}$, but where some instruments, z, are available such that with z is independent of u (Berkson error) and E ( u$_{y}$ | z ) = 0 . Denote the density of x by f$_{x}$, density of z by f$_{z}$, density of u by f u and correspondingly 5