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 | References | Similar Articles | Additional Information

Abstract: For a function *f* analytic in the closed disc , we study the behavior of zeros of the successive iterates , where . 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