Convergence of diagonal Padé approximants

Let $\mu$ be a positive measure with compact support contained in $\mathbf R$, and set
$$ \widehat\mu(z)=\int(z-x)^{-1}\,d\mu(x). $$

This paper studies the convergence of diagonal Padé approximants for meromorphic functions of the form $f(z)=\widehat\mu(z)+r(z)$, where $r(z)$ is a rational function.
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