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Boundary behaviour of functions which possess universal Taylor series
Author(s) -
Gardiner Stephen J.
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds078
Subject(s) - taylor series , mathematics , holomorphic function , boundary (topology) , series (stratigraphy) , complement (music) , complex plane , simply connected space , pure mathematics , mathematical analysis , series expansion , paleontology , biochemistry , chemistry , complementation , gene , biology , phenotype
It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess ‘universal’ Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\ Ω that have connected complement. This paper establishes a strong unboundedness property for such functions near every boundary point. The result is new even in the case of the disc, where it strengthens work of several authors.