Polya-Schur master theorems for circular domains and their boundaries

被引：61

作者：

Borcea, Julius ^{[1
]}

Branden, Petter ^{[2
]}

机构：

[1] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden

[2] Royal Inst Technol, Dept Math, SE-10044 Stockholm, Sweden

来源：

ANNALS OF MATHEMATICS | 2009年 / 170卷 / 01期

关键词：

TRANSFORMED POLYNOMIALS; LINEAR TRANSFORMATIONS; MULTIPLIER SEQUENCES; ALGEBRAIC EQUATIONS; ZEROS; OPERATORS;

D O I：

10.4007/annals.2009.170.465

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize all linear operators on finite or infinite-dimensional polynomial spaces that preserve the property of having the zero set inside a prescribed region Omega subset of C for arbitrary closed circular domains Omega (i.e., images of the closed unit disk under a Mobius transformation) and their boundaries. This provides a natural framework for dealing with several long-standing fundamental problems, which we solve in a unified way. In particular, for Omega = R our results settle open questions that go back to Laguerre and Polya-Schur.

引用

页码：465 / 492

页数：28

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