Abstract.
Let {r n } be a sequence of rational functions deg( r n ≤ n) that converge rapidly in measure to an analytic function f on an open set in C N . We show that {r n } converges rapidly in capacity to f on its natural domain of definition W f (which, by a result of Goncar, is an open subset of C N ).
In particular, for f meromorphic on C N and analytic near zero the sequence of Padé approximants {π n (z, f, λ)} (as defined by Goncar) converges rapidly in capacity to f on C N .
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January 14, 1999. Date revised: October 7, 1999. Date accepted: November 1, 1999.
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Bloom, T. On the Convergence in Capacity of Rational Approximants. Constr. Approx. 17, 91–102 (2001). https://doi.org/10.1007/s003650010011
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DOI: https://doi.org/10.1007/s003650010011