A transform of finite order entire functions and perturbations of zeros

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Abstract

A new transform of finite order entire functions is introduced. In terms of that transform and the Taylor coefficients, perturbation results are established. In addition, the conditions that provide conservation of the total multiplicities of the zeros in some domains are investigated. The results obtained in this article enable us to estimate the distances between the zeros of entire functions and the zeros of their derivatives. They also enable us to explore the relations between the zeros of power series, their partial sums and tails.

Original languageEnglish
Pages (from-to)493-509
Number of pages17
JournalComplex Variables and Elliptic Equations
Volume54
Issue number5
DOIs
StatePublished - 1 May 2009

Keywords

  • Bounds for zeros
  • Conservation of multiplicities
  • Critical points
  • Finite order entire functions
  • Perturbations, partial sums
  • Tails of the Taylor series

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