Unify continuation theorems across compactifications

Develop a single theorem encompassing the surveyed analytic-continuation results for power series, including continuation to bounded and unbounded domains and continuation on the Riemann surface of the logarithm.

Background

The paper presents separate frameworks for analytic continuation to bounded subsets of the complex plane, unbounded domains, and the Riemann surface of the logarithm. These frameworks use different compactifications, support functions, and growth conditions for coefficient interpolants.

The author identifies as an unresolved question whether these results can be unified into one theorem. The proposed unification would require a common treatment of the distinct compactifications and asymptotic hypotheses appearing throughout the survey.

References

More broadly, the unified formulations developed here raise the question whether a single theorem can encompass all the continuation results surveyed in this paper, including those for bounded and unbounded continuation domains and for the Riemann surface of the logarithm.

— When can a power series be analytically continued?  (2609.16676 - Beauduin, 15 Sep 2026) in Section 5, Further directions and references