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Pointwise limits of analytic functions
Author(s) -
Davie A. M.
Publication year - 2007
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/jlms/jdl014
Subject(s) - pointwise , limit (mathematics) , mathematics , limit point , context (archaeology) , pointwise convergence , complex plane , analytic function , pure mathematics , sequence (biology) , uniform limit theorem , limit of a sequence , mathematical analysis , computer science , paleontology , approx , genetics , biology , operating system
We characterise those complex‐valued functions on an open subset D of the complex plane which can be expressed as the limit of a sequence of analytic functions converging at each point of D . Partial results are given for a generalisation of this question to pointwise limits of a quite general algebra of functions. In this general context, we are also able to characterise analogues of the higher Baire classes (pointwise limits of pointwise limits, etc.).