On a generalization of Jentzsch's theorem

Blatt, Hans-Peter; Blatt, Simon; Luh, Wolfgang

doi:doi:10.1016/j.jat.2008.11.016

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On a generalization of Jentzsch's theorem

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Blatt, Simon
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Blatt, H.-P., Blatt, S., & Luh, W. (2009). On a generalization of Jentzsch's theorem. Journal of Approximation Theory, 159(1 Sp. Iss. Sp. Iss. SI), 26-38. doi:doi:10.1016/j.jat.2008.11.016.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-6471-2

Abstract

Let E be a compact subset of View the MathML source with connected, regular complement View the MathML source and let G(z) denote Green’s function of Ω with pole at ∞. For a sequence (pn)nset membership, variantΛ of polynomials with degpn=n, we investigate the value-distribution of pn in a neighbourhood U of a boundary point z0 of E if G(z) is an exact harmonic majorant of the subharmonic functions View the MathML source in View the MathML source. The result holds for partial sums of power series, best polynomial approximations, maximally convergent polynomials and can be extended to rational functions with a bounded number of poles.