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Borcea's variance conjectures on the critical points of polynomials | | Dmitry Khavinson
; Rajesh Pereira
; Mihai Putinar
; Edward B. Saff
; Serguei Shimorin
; | | Date: |
25 Oct 2010 | | Abstract: | Closely following recent ideas of J. Borcea, we discuss various modifications
and relaxations of Sendov’s conjecture about the location of critical points of
a polynomial with complex coefficients. The resulting open problems are
formulated in terms of matrix theory, mathematical statistics or potential
theory. Quite a few links between classical works in the geometry of
polynomials and recent advances in the location of spectra of small rank
perturbations of structured matrices are established. A couple of simple
examples provide natural and sometimes sharp bounds for the proposed
conjectures. | | Source: | arXiv, 1010.5167 | | Services: | Forum | Review | PDF | Favorites | |
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