Power series and nonnormal functions
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- by J. S. Hwang and Peter Lappan PDF
- Proc. Amer. Math. Soc. 97 (1986), 265-268 Request permission
Abstract:
We construct a sequence $\left \{ {{a_n}} \right \}$ of positive numbers such that ${a_n} \to 0,\sum {\left | {{a_n} - {a_{n - 1}}} \right | < \infty }$, and the function $f(z) = \sum {{a_n}{z^n}}$ is not a normal function. This answers a question raised by the second author (Proc. Amer. Math. Soc. 85 (1982), 335-341).References
- Peter Lappan, Coefficients and normal functions, Proc. Amer. Math. Soc. 85 (1982), no. 3, 335–341. MR 656097, DOI 10.1090/S0002-9939-1982-0656097-6
- Peter Lappan, Normal functions with bounded coefficients, Analysis 3 (1983), no. 1-4, 305–315. MR 756120, DOI 10.1524/anly.1983.3.14.305
- Olli Lehto and K. I. Virtanen, Boundary behaviour and normal meromorphic functions, Acta Math. 97 (1957), 47–65. MR 87746, DOI 10.1007/BF02392392
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 265-268
- MSC: Primary 30D45; Secondary 30B40
- DOI: https://doi.org/10.1090/S0002-9939-1986-0835877-1
- MathSciNet review: 835877