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- W3136131927 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 ({mathbb {R}}) onto itself such that (h^{-1}) is not symmetric. This implies that the set of all symmetric self-homeomorphisms of ({mathbb {R}}) does not constitute a group under the composition. We also consider the same problem for a strongly symmetric self-homeomorphism of ({mathbb {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." @default.
- W3136131927 created "2021-03-29" @default.
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- W3136131927 date "2021-03-12" @default.
- W3136131927 modified "2023-10-08" @default.
- W3136131927 title "Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion" @default.
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- W3136131927 doi "https://doi.org/10.1007/s13324-021-00510-7" @default.
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