A Conjectured Analogue of Rolle's Theorem for Polynomials with Real or Complex Coefficients

DOI10.2307/2322536zbMath0627.30001OpenAlexW4237171007MaRDI QIDQ3031061

I. J. Schoenberg

Publication date: 1986

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2322536

zbMATH Keywords

Rolle's theorem

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Inequalities in the complex plane (30A10)

Related Items (13)

Circulants and critical points of polynomials ⋮ Skew-circulant matrix and critical points of polynomials ⋮ Differentiators and the geometry of polynomials. ⋮ Integrability of diagonalizable matrices and a dual Schoenberg type inequality ⋮ A companion matrix approach to the study of zeros and critical points of a polynomial ⋮ Integrators of matrices ⋮ Remarks on circulant matrices and critical points of polynomials ⋮ Inverse spectral problem for normal matrices and the Gauss-Lucas theorem ⋮ On some properties of the Abel–Goncharov polynomials and the Casas-Alvero problem ⋮ Extremal Problems for Polynomials in the Complex Plane ⋮ Four Theorems with Their Foci on Ellipses ⋮ On a Schoenberg-type conjecture ⋮ A Rolle's theorem for real exponential polynomials in the complex domain

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