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arXiv · 1111.2209

Linear operators on polynomials preserving roots in open circular domains

Eugeny Melamud
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Abstract

In the present paper we answer a question raised by J. Borcea and P. Branden and give a description of the class of operators preserving roots in open circular domains, i.e., in images of the open upper half-plane under the Mobius transformations. Our second result is a description of the difference between $\Apr(G)$ (the class of operators preserving roots in an open set $G$) and $\Apr(\bar G)$ (the class of operators preserving roots in $\bar{G}$).

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Eugeny Melamud. 2011-11-09. Linear operators on polynomials preserving roots in open circular domains. https://arxiv.org/abs/1111.2209

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