A transform of finite order entire functions and perturbations of zeros

M. I. Gil

doi:10.1080/17476930902763777

A transform of finite order entire functions and perturbations of zeros

M. I. Gil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	493-509
Number of pages	17
Journal	Complex Variables and Elliptic Equations
Volume	54
Issue number	5
DOIs	https://doi.org/10.1080/17476930902763777
State	Published - 1 May 2009

Keywords

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

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1080/17476930902763777

Cite this

@article{299d926fb95049579c6f1ea44746e8d7,

title = "A transform of finite order entire functions and perturbations of zeros",

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.",

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

author = "Gil, {M. I.}",

note = "Funding Information: This research was supported by the Kamea Fund of Israel.",

year = "2009",

month = may,

day = "1",

doi = "10.1080/17476930902763777",

language = "English",

volume = "54",

pages = "493--509",

journal = "Complex Variables and Elliptic Equations",

issn = "1747-6933",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

TY - JOUR

T1 - A transform of finite order entire functions and perturbations of zeros

AU - Gil, M. I.

N1 - Funding Information: This research was supported by the Kamea Fund of Israel.

PY - 2009/5/1

Y1 - 2009/5/1

N2 - 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.

AB - 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.

KW - Bounds for zeros

KW - Conservation of multiplicities

KW - Critical points

KW - Finite order entire functions

KW - Perturbations, partial sums

KW - Tails of the Taylor series

UR - http://www.scopus.com/inward/record.url?scp=67651244216&partnerID=8YFLogxK

U2 - 10.1080/17476930902763777

DO - 10.1080/17476930902763777

M3 - Article

AN - SCOPUS:67651244216

SN - 1747-6933

VL - 54

SP - 493

EP - 509

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 5

ER -

A transform of finite order entire functions and perturbations of zeros

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this