Abstract by Jason White
Zero-Sector Reducing Operators
We state a Jensen-disc type theorem for polynomials with real coefficients 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 which map real polynomials with their zeros in a closed convex sector to polynomials with zeros in a smaller sector. We, therefore, provide the first example of a zero-sector reducing operator.