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Proceedings of the American Mathematical Society

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Zeros of successive derivatives and iterated operators on analytic functions


Authors: J. K. Shaw and C. L. Prather
Journal: Proc. Amer. Math. Soc. 79 (1980), 225-232
MSC: Primary 30C15
DOI: https://doi.org/10.1090/S0002-9939-1980-0565344-9
MathSciNet review: 565344
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Abstract: For a function f analytic in the closed disc $ \vert z\vert \leqslant 1$, we study the behavior of zeros of the successive iterates $ ({\theta ^n}f)(z),n = 0,1,2, \ldots$, where $ \theta = {(z + \alpha )^{p + 1}}d/dz$. We find that such behavior closely parallels that for the ordinary derivative operator. Using change-of-variable methods, we obtain information on zeros of derivatives of functions analytic in half-planes.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0565344-9
Keywords: Zeros of derivatives, zero-free regions, differential operators
Article copyright: © Copyright 1980 American Mathematical Society

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