Pointwise limits of analytic functions

• Autores: A. M. Davie
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 75, Nº 1, 2007, págs. 133-145
• Idioma: inglés
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• Resumen

  • 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.)