Generalized Rolle theorem in \({\mathbb{R}}^n\) and \({\mathbb{C}}\)

DOI10.1007/BF02259625zbMath0941.26009OpenAlexW2032587018MaRDI QIDQ1972708

Sergey Yu. Yakovenko, A. G. Khovanskii

Publication date: 13 April 2000

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02259625

zbMATH Keywords

analytic functionLucas theoremVoorhoeve indexabsolute integral curvatureBernstein indexcomplex isolated zeros of quasipolynomialsmultidimensional generalization of the Rolle theoremsmooth spatial curve

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) Integration of real functions of several variables: length, area, volume (26B15) Integral geometry (53C65) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05)

Related Items (10)

On extended Chebyshev systems with positive accuracy ⋮ On global non-oscillation of linear ordinary differential equations with polynomial coefficients ⋮ Unnamed Item ⋮ On local behavior of analytic functions ⋮ Integral curvatures, oscillation and rotation of spatial curves around affine subspaces ⋮ Restricted infinitesimal Hilbert's sixteenth problem ⋮ Exponential Gelfond–Khovanskii formula in dimension one ⋮ Complex cellular structures ⋮ A version of Rolle's theorem and applications ⋮ A Rolle type theorem for cyclicity of zeros of families of analytic functions

Cites Work

• Unnamed Item
• A Complex Analogue of the Rolle Theorem and Polynomial Envelopes of Irreducible Differential Equations in the Complex Domain
• On total curvatures of closed space curves

This page was built for publication: Generalized Rolle theorem in \({\mathbb{R}}^n\) and \({\mathbb{C}}\)