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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the tangential speed of parabolic semigroups of holomorphic functions
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by Konstantinos Zarvalis PDF
Proc. Amer. Math. Soc. 149 (2021), 729-737 Request permission

Abstract:

We prove that there is a parabolic semigroup $(\phi _t)$ in $\mathbb {D}$ of positive hyperbolic step, such that its tangential speed $\nu ^T(t)$ does not satisfy $|\nu ^T(t)-\frac {1}{2}\log t|<C, \;\; t\ge 1$, for any positive constant $C$. This result answers in the negative a question posed by F. Bracci.
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Additional Information
  • Konstantinos Zarvalis
  • Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece
  • Email: zarkonath@math.auth.gr
  • Received by editor(s): April 8, 2020
  • Received by editor(s) in revised form: May 31, 2020
  • Published electronically: December 8, 2020
  • Communicated by: Filippo Bracci
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 729-737
  • MSC (2020): Primary 37F44, 30D05
  • DOI: https://doi.org/10.1090/proc/15238
  • MathSciNet review: 4198078