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Zbl 1236.41014
Blatt, Hans-Peter; Kovacheva, Ralitza K.
Growth behavior and zero distribution of rational approximants.
(English)
[J] Constr. Approx. 34, No. 3, 393-420 (2011). ISSN 0176-4276; ISSN 1432-0940/e

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-Szeg\H{o} 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.
[Francisco Pérez Acosta (La Laguna)]
MSC 2000:
*41A20 Approximation by rational functions
26C15 Rational functions (real variables)
30E10 Approximation in the complex domain
41A25 Degree of approximation, etc.

Keywords: rational approximation; distribution of zeros; Jentzsch-Szeg\H{o}-type theorems; Padé approximation; $m_1$-maximal convergence; harmonic majorants

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