Abstract
We show that interpolation to a function, analytic on a compact setE in the complex plane, can yield maximal convergence only if a subsequence of the interpolation points converges to the equilibrium distribution onE in the weak sense. Furthermore, we will derive a converse theorem for the case when the measure associated with the interpolation points converges to a measure onE, which may be different from the equilibrium measure.
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Grothmann, R. Distribution of interpolation points. Ark. Mat. 34, 103–117 (1996). https://doi.org/10.1007/BF02559510
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DOI: https://doi.org/10.1007/BF02559510