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.References
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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