Linear 𝑞-difference, difference and differential operators preserving some 𝒜-entire functions

Author:

Huang Jiaxing,Ng Tuen-Wai

Abstract

We apply Rossi’s half-plane version of Borel’s theorem to study the zero distribution of linear combinations of A \mathcal {A} -entire functions (Theorem 1.2). This provides a unified way to study linear q q -difference, difference and differential operators (with entire coefficients) preserving subsets of A \mathcal {A} -entire functions, and hence obtain several analogous results for the Hermite-Poulain theorem to linear finite ( q q -)difference operators with polynomial coefficients. The method also produces a result on the existence of infinitely many non-real zeros of some differential polynomials of functions in certain sub-classes of A \mathcal {A} -entire functions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference35 articles.

1. A note on Wronskians and linear dependence of entire functions in 𝐶ⁿ;Berenstein, Carlos;Complex Variables Theory Appl.,1994

2. Real entire functions of infinite order and a conjecture of Wiman;Bergweiler, W.;Geom. Funct. Anal.,2003

3. W. Bergweiler, A. Eremenko, and J. K. Langley, Zeros of differential polynomials in real meromorphic functions, Proc. Edinburgh Math. Soc. 48 (2005), 279–293.

4. On the zeros of the second derivative of real entire functions;Bergweiler, W.;J. Anal.,1993

5. Meromorphic solutions of some functional equations;Bergweiler, Walter;Methods Appl. Anal.,1998

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3