Converse Sturm-Hurwitz-Kellogg theorem and related results

Research output: Contribution to journalArticle

Abstract

We prove that if V n is a Chebyshev system on the circle and f is a continuous real-valued function with at least n + 1 sign changes then there exists an orientation preserving diffeomorphism of S 1 that takes f to a function L 2-orthogonal to V. We also prove that if f is a function on the real projective line with at least four sign changes then there exists an orientation preserving diffeomorphism of ℝℙ1 that takes f to the Schwarzian derivative of a function on ℝℙ1. We show that the space of piecewise constant functions on an interval with values ± 1 and at most n + 1 intervals of constant sign is homeomorphic to n-dimensional sphere.

Original languageEnglish (US)
Pages (from-to)121-130
Number of pages10
JournalJournal of Fixed Point Theory and Applications
Volume3
Issue number1
DOIs
StatePublished - May 1 2008

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics

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