Asymptotic behavior of functions with bounded boundary rotation
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- by James W. Noonan PDF
- Trans. Amer. Math. Soc. 164 (1972), 397-410 Request permission
Abstract:
For $k \geqq 2$ denote by ${V_k}$ the class of normalized functions, analytic in the unit disc, which have boundary rotation at most $k\pi$. Let ${a_n}$ be the nth Taylor coefficient of $f(z) \in {V_k}$. Let ${I_\lambda }(r,f’)$ and ${I_\lambda }(r,f)$ be the $\lambda$-integral mean of $f’(z)$ and $f(z)$ respectively. We determine asymptotic formulas for $f’(z)$, and these formulas are then applied to study the behavior of $|{a_n}|$ as $n \to \infty$, and the behavior of ${I_\lambda }(r,f’)$ and ${I_\lambda }(r,f)$ as $r \to 1$.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 164 (1972), 397-410
- MSC: Primary 30A32
- DOI: https://doi.org/10.1090/S0002-9947-1972-0294618-4
- MathSciNet review: 0294618