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Growth behavior and zero distribution of rational approximants. (English) Zbl 1236.41014
From authors’ abstract: The authors investigate the growth and the distribution of zeros of rational uniform approximations with numerator degree $\leq n$ and denominator degree $\leq m_{n}$ for meromorphic functions $f$ on a compact set $E$ of $\mathbb{C}$ where $m_{n} = o(n/\log n)$ as $n \rightarrow \infty$. They obtain a Jentzsch-Szegő type result, i.e., the zero distribution converges weakly to the equilibrium distribution of the maximal Green domain $E_{\rho(f)}$ of meromorphy of $f$ if $f$ has a singularity of multivalued character on the boundary of $E_{\rho(f)}$. The paper extends results for polynomial approximation and rational approximation with fixed degree of the denominator. As applications, Padé approximation and real rational best approximants are considered.

41A20Approximation by rational functions
26C15Rational functions (real variables)
30E10Approximation in the complex domain
41A21Padé approximation
41A25Rate of convergence, degree of approximation
Full Text: DOI
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