In weighted Bergman spaces, equally spaced poles minimize the norm of high-degree simple partial fractions exactly when the first N^2-2 moments vanish, and this fails in general.
Approximation by simple partial fractions in unbounded domains
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High degree simple partial fractions in the Bergman space: Approximation and Optimization
In weighted Bergman spaces, equally spaced poles minimize the norm of high-degree simple partial fractions exactly when the first N^2-2 moments vanish, and this fails in general.