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A Strong Notion of Universal Taylor Series
Author(s) -
Nestoridis V.
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004782
Subject(s) - holomorphic function , combinatorics , taylor series , center (category theory) , mathematics , series (stratigraphy) , unit (ring theory) , polynomial , sequence (biology) , unit circle , function (biology) , physics , pure mathematics , mathematical analysis , crystallography , paleontology , chemistry , genetics , mathematics education , evolutionary biology , biology
For a holomorphic function f in the open unit disc D , the N th partial sum of its Taylor series with center ζ ∈ D is denoted by S N ( f ,ζ)( z )=∑ n = 0 N ( f ( n ) ( ζ ) / n ! ) ( z − ζ ) n . Generically, all functions f in H ( D ) satisfy the following. For every compact set K ⊂ C with K ∩ D =Ø and K c connected and every polynomial h , there exists a sequence of positive integers{ λ n } ∞such that, for every 1 ∈ {0,1,2,…},sup z ∈ K|∂ l∂ z lS λ n ( f , 0 ) ( z ) − h ( l )( z )| → 0 as n → + ∞ .