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Quantitative Bounds for Hurwitz Stable Polynomials under Multiplier Transformations Spur Final Paper
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zhu, Xuwen |
| Copyright Year | 2015 |
| Abstract | We extend results of Borcea and Brändén to quantitatively bound the movement of the zeros of Hurwitz stable polynomials under linear multiplier operators. For a multiplier operator T on polynomials of degree up to n, we show that the ratio between the maximal real part of the zeros of a Hurwitz stable polynomial f and that of its transform T [f ] is minimized for the polynomial (z + 1). For T operating on polynomials of all degrees, we use the classical PólyaSchur theorem to derive an asymptotic formula for the maximal real part of the zeros of T [(z+1)], and consider the action of T on classes of entire functions. We develop interlacing controls on the transformations of real-rooted polynomials. On the basis of numerical evidence, we conjecture several further quantitative controls on the zeros of Hurwitz stable polynomials under multiplier operators. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://math.mit.edu/research/undergraduate/spur/documents/2014graham.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
