On zero-sector reducing operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:468

Article

Cardon, David A.¹  Forgacs, Tamas²  Piotrowski, Andrzej³  Sorensen, Evan¹  White, Jason C.¹ 

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Dept Math, M-S PB108, Fresno, CA 93740 USA

[3] Univ Alaska Southeast, Dept Nat Sci, M-S SOB1, Juneau, AK 99801 USA

关键词: Zeros;    Entire functions;    Jensen disc;    Zero-sector reducing operator;    Multiplier sequences;   

DOI  :  10.1016/j.jmaa.2018.08.025

来源: Elsevier

【 摘 要 】

We prove a Jensen-disc type theorem for polynomials p is an element of R[z] having all their zeros in a sector of the complex plane. This result is then used to prove the existence of a collection of linear operators T: R[z] -> R[z] which map polynomials with their zeros in a closed convex sector vertical bar arg z vertical bar <= theta < pi/2 to polynomials with zeros in a smaller sector vertical bar arg z vertical bar <= gamma < theta. We, therefore, provide the first example of a zero-sector reducing operator. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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