  We present a method for analytic continuation of retarded Green functions,
including Euclidean Green functions computed using lattice QCD. The method is
based on conformal maps and construction of an interpolation function which is
analytic in the upper half plane. A novel aspect of our method is rigorous
bounding of systematic uncertainties, which are handled by constructing the
full space of interpolating functions (at each point in the upper half-plane)
consistent with the given Euclidean data and the constraints of analyticity.
The resulting Green function in the upper half-plane has an appealing
interpretation as a smeared spectral function.
