On Zero-Sector Reducing Operators

2018/02/07 by David A. Cardon, Cardon, David A., Tamás Forgács +7
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1802.02641

11 pages, 3 figures

arxiv created 2018/02/07 · arxiv updated 2018/02/09

Abstract

We prove a Jensen-disc type theorem for polynomials p∈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\colonℝ[z]→ℝ[z] which map polynomials with their zeros in a closed convex sector |arg z| ≤ θ<π/2 to polynomials with zeros in a smaller sector |arg z| ≤ γ<θ. We, therefore, provide the first example of a zero-sector reducing operator.

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