Adding a discrete measure to an absolute continuous one (with respect to
the volume element of an algebraic set) raises non-trivial questions about the bounds and growth of the original, versus perturbed, Christoffel-Darboux kernels. In the fortunate case of perturbing full Euclidean volume of a domain, pluripotential theory and more refined tools from approximation theory provide accurate estimates. Based on recent work with B. Beckermann and Ed Saff.
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