Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion

Huaying Wei, Katsuhiko Matsuzaki

Research output: Contribution to journalArticlepeer-review

Abstract

A quasisymmetric homeomorphism defines an element of the universal Teichmüller space and a symmetric one belongs to its little subspace. We show an example of a symmetric homeomorphism h of the real line R onto itself such that h- 1 is not symmetric. This implies that the set of all symmetric self-homeomorphisms of R does not constitute a group under the composition. We also consider the same problem for a strongly symmetric self-homeomorphism of R which is defined by a certain concept of harmonic analysis. These results reveal the difference of the sets of such self-homeomorphisms of the real line from those of the unit circle.

Original languageEnglish
Article number79
JournalAnalysis and Mathematical Physics
Volume11
Issue number2
DOIs
Publication statusPublished - 2021 Jun

Keywords

  • Asymptotically conformal
  • Characteristic topological subgroup
  • Quasisymmetric
  • Strongly symmetric
  • Symmetric homeomorphism
  • VMO

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion'. Together they form a unique fingerprint.

Cite this