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

Huaying Wei, Katsuhiko Matsuzaki*

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
論文番号79
ジャーナルAnalysis and Mathematical Physics
11
2
DOI
出版ステータスPublished - 2021 6月

ASJC Scopus subject areas

  • 分析
  • 代数と数論
  • 数理物理学

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