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2019 On Jack's lemma
Richard Fournier
Rocky Mountain J. Math. 49(6): 1869-1875 (2019). DOI: 10.1216/RMJ-2019-49-6-1869

Abstract

We give a new proof and minor refinements, in the polynomial case, of Jack's lemma. This proof is essentially based on the Bernstein's inequality for polynomials on the unit circle. We also discuss the cases of equality of \[ \frac {d^2}{d \theta ^2} \ln | {f(e^{i\theta })}| \leq 0, \] where $f$ is analytic in the unit disc and in a neighborhood of $e^{i\theta }$ where $|{f(e^{i\theta })}|=\sup _{|z|\lt 1}|f(z)|$.

Citation

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Richard Fournier. "On Jack's lemma." Rocky Mountain J. Math. 49 (6) 1869 - 1875, 2019. https://doi.org/10.1216/RMJ-2019-49-6-1869

Information

Published: 2019
First available in Project Euclid: 3 November 2019

zbMATH: 07136583
MathSciNet: MR4027238
Digital Object Identifier: 10.1216/RMJ-2019-49-6-1869

Subjects:
Primary: 30C10, 30C80

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 6 • 2019
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