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Convexity properties of twisted root maps
 math.CA/0312321. ORDER AND ISOTONIC DIFFERENTIAL OPERATORS 21
"... Abstract. The strong spectral order induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We prove that twisted root maps associated with linear operators acting on Hn are G˚arding convex on every polynomial pencil and we characterize the class of polynom ..."
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Abstract. The strong spectral order induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We prove that twisted root maps associated with linear operators acting on Hn are G˚arding convex on every polynomial pencil and we characterize the class of polynomial pencils of logarithmic derivative type by means of the strong spectral order. Let A ′ be the monoid of linear operators that preserve hyperbolicity as well as root sums. We show that any polynomial in Hn is the global minimum of its A ′orbit and we conjecture a similar result for complex polynomials.
unknown title
, 2009
"... On the number of real critical points of logarithmic derivatives and the Hawaii conjecture ..."
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On the number of real critical points of logarithmic derivatives and the Hawaii conjecture
unknown title
, 2009
"... On the number of real critical points of logarithmic derivatives and the Hawaii conjecture ..."
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On the number of real critical points of logarithmic derivatives and the Hawaii conjecture