Products of parametric extensions: refined estimates

We present point wise estimates on approximation by bounded linear operators of real-valued continuous functions defined on the cartesian product of d compact intervals. The main purpose is to provide a unified theory to deal with pointwise estimates on approximation processes of the above type which are generated by the tensor product method. This will constitute an extension and a refinement of earlier work of Haussmann and Pottinger. As an example a new estimate for approximation by multivariate positive linear operators is given.