Differentiators and the geometry of polynomials |
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Authors: | Rajesh Pereira |
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Affiliation: | University of Toronto, Toronto, Canada M5S 3G3 |
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Abstract: | In 1959, Davis introduced the concept of a differentiator of an operator on a finite-dimensional Hilbert space. We prove that every such operator possesses a differentiator. We also use the theory of differentiators to solve several problems in the geometry of polynomials. For instance, we answer in the affirmative a twenty year old unsolved conjecture of Schoenberg, a related conjecture of Katsoprinakis and a fifty year old unsolved conjecture of De Bruijn and Springer. |
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Keywords: | Differentiators Geometry of polynomials Schoenberg's conjecture De  Bruijn-Springer conjecture Majorization order |
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