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# Growth behaviour and zero distribution of rational approximants

## Titelangaben

Blatt, Hans-Peter ; Kovacheva, Ralitza K.:
Growth behaviour and zero distribution of rational approximants.
In: Constructive approximation. 34 (2010). - S. 393-420.
ISSN 0176-4276 ; 1432-0940

## Volltext

We 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 $\CC$ where $m_n = o(n/\log n)$ as $n \rightarrow \infty$. We 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.
Publikationsform: Artikel Rational approximation, distribution of zeros, Jentzsch-Szeg\H{o}-Type Theorems, Padé approximation, $m_1$-maximal convergence, harmonic majorants Deutsch Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Angewandte Mathematik Ja Springer Ja 4566