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arXiv · 1802.02641

On Zero-Sector Reducing Operators

David A. Cardon·Tamás Forgács·Andrzej Piotrowski·Evan Sorensen·Jason C. White
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Abstract

We prove a Jensen-disc type theorem for polynomials $p\in\mathbb{R}[z]$ 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 $T\colon\mathbb{R}[z]\to\mathbb{R}[z]$ which map polynomials with their zeros in a closed convex sector $|\arg z| \leq \theta<\pi/2$ to polynomials with zeros in a smaller sector $|\arg z| \leq \gamma<\theta$. We, therefore, provide the first example of a zero-sector reducing operator.

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David A. Cardon, Tamás Forgács, Andrzej Piotrowski, Evan Sorensen, Jason C. White. 2018-02-07. On Zero-Sector Reducing Operators. https://arxiv.org/abs/1802.02641

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