Obreschkoff's theorem revisited: What convex sets are contained in the set of hyperbolic polynomials?

DOI10.1016/0022-4049(92)90060-SzbMath0772.12002OpenAlexW2038682142MaRDI QIDQ1207527

Jean-Pierre Dedieu

Publication date: 1 April 1993

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(92)90060-s

zbMATH Keywords

convexityexplicit boundreal rootsroot separationhyperbolic polynomialspolygonal pathObreschkoff's theorempolynomials with real coefficients

Mathematics Subject Classification ID

Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Real polynomials: location of zeros (26C10)

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Interlacing families. III: Sharper restricted invertibility estimates ⋮ Interlacing Families IV: Bipartite Ramanujan Graphs of All Sizes ⋮ The roots of the independence polynomial of a clawfree graph ⋮ Combinatorics \(\&\) topology of stratifications of the space of monic polynomials with real coefficients ⋮ Mixed determinants and the Kadison-Singer problem ⋮ Derivation of the real-rootedness of coordinator polynomials from the Hermite-Biehler theorem ⋮ Wronskian-based tests for stability of polynomial combinations ⋮ Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions ⋮ Maximal univalent disks of real rational functions and Hermite-Biehler polynomials ⋮ Nonnegative polynomials and their Carathéodory number ⋮ On operators on polynomials preserving real-rootedness and the Neggers-Stanley conjecture ⋮ On the largest eigenvalue of a mixed graph with partial orientation ⋮ Convexity properties of twisted root maps ⋮ On linear transformations preserving the Pólya frequency property ⋮ Interlacing families. I: Bipartite Ramanujan graphs of all degrees ⋮ Interlacing families. II: Mixed characteristic polynomials and the Kadison-Singer problem ⋮ Corrigendum: Obreschkoff's theorem revisited: What convex sets are contained in the set of hyperbolic polynomials?

Cites Work

• Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets
• Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix
• Hyperbolic polynomials and Vandermonde mappings
• On the geometric properties of Vandermonde's mapping and on the problem of moments
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