Journal d'Analyse Mathématique

, Volume 133, Issue 1, pp 27–49 | Cite as

Generalised continuation by means of right limits

  • David Sauzin
  • Giulio Tiozzo


Several theories have been proposed to generalise the concept of analytic continuation to holomorphic functions of the disc for which the circle is a natural boundary. Elaborating on Breuer-Simon’s work on right limits of power series, Baladi-Marmi-Sauzin recently introduced the notion of renascent right limit and rrl-continuation. We discuss a few examples and consider particularly the classical example of Poincaré simple pole series in this light. These functions are represented in the disc as series of infinitely many simple poles located on the circle; they appear, for instance, in small divisor problems in dynamics. We prove that any such function admits a unique rrl-continuation, which coincides with the function obtained outside the disc by summing the simple pole expansion. We also discuss the relation with monogenic regularity in the sense of Borel.


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Copyright information

© Hebrew University Magnes Press 2017

Authors and Affiliations

  1. 1.CNRS IMCCE, Observatoire de ParisParisFrance
  2. 2.University of TorontoTorontoCanada

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