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ID: 442637.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
On a generalization of Jentzsch's theorem
Authors:Blatt, Hans-Peter; Blatt, Simon; Luh, Wolfgang
Date of Publication (YYYY-MM-DD):2009-07
Title of Journal:Journal of Approximation Theory
Volume:159
Issue / Number:1 Sp. Iss. Sp. Iss. SI
Start Page:26
End Page:38
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
Identifiers:ISI:000267132100003 [ID No:1]
ISSN:0021-9045 [ID No:2]
DOI:doi:10.1016/j.jat.2008.11.016
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