Constrained energy problems with applications to orthogonal polynomials of a discrete variable

Given a positive measure Σ with gs > 1, we write Με ℳΣ if Μ is a probability measure and Σ—Μ is a positive measure. Under some general assumptions on the constraining measure Σ and a weight functionw, we prove existence and uniqueness of a measure λΣw that minimizes the weighted logarithmic energy over the class ℳΣ. We also obtain a characterization theorem, a saturation result and a balayage representation for the measure λΣw As applications of our results, we determine the (normalized) limiting zero distribution for ray sequences of a class of orthogonal polynomials of a discrete variable. Explicit results are given for the class of Krawtchouk polynomials.