LOCATION OF ZEROS PART I: REAL POLYNOMIALS AND ENTIRE FUNCTIONS
LOCATION OF ZEROS PART I: REAL POLYNOMIALS AND ENTIRE FUNCTIONS
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DOI：
10.1215/ijm/1256046494
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发表时间：
1983-06
影响因子：
0.6
通讯作者：
T. Craven;G. Csordas
中科院分区：
文献类型：
--
作者：
T. Craven;G. Csordas
在研究多项式和整个函数的零点分布时，所使用的技术大致分为三大类：解析法、几何法和代数法。在本文中，这代表了一个两部分调查的第一部分，我们将试图利用所有三种技术的优势。在第2节中，我们将介绍一种新的几何工具（参见[3]）来证明大多数情况下难以用代数或解析方法解决的结果。此外，几何定理通常比作为推论推导出来的代数定理更强。在处理实多项式（和实整个函数）零点位置的大量文献中，线性变换T起着重要的作用，它具有以下性质：（1.1）Zc(T[fl) < Zc(f)；
In the study of the distribution of zeros of polynomials and entire functions the techniques used, roughly speaking, fall into three categories" analytic, geometric and algebraic. In this paper, which represents the first portion of a two-part investigation, we will attempt to exploit the advantages of all three techniques. In Section 2 we will introduce a novel geometric tool (see also [3]) to prove results which, for the most part, are intractable by algebraic or analytic methods. In addition, the geometric theorems are generally stronger than their algebraic counterparts which are derived as corollaries. In the extensive literature dealing with the location of zeros of real polynomials (and real entire functions) a significant role is played by linear transformations T which possess the following property: (1.1) Zc(T[fl) < Zc(f),