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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 n and denominator degree m n for meromorphic functions f on a compact set E of where m n =o(n/logn) as n. They obtain a Jentzsch-Szegő type result, i.e., the zero distribution converges weakly to the equilibrium distribution of the maximal Green domain E ρ(f) of meromorphy of f if f has a singularity of multivalued character on the boundary of E ρ(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.
MSC:
41A20Approximation by rational functions
26C15Rational functions (real variables)
30E10Approximation in the complex domain
41A21Padé approximation
41A25Rate of convergence, degree of approximation
References:
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