TY - JOUR
T1 - Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion
AU - Wei, Huaying
AU - Matsuzaki, Katsuhiko
N1 - Funding Information:
H. Wei: Research supported by the National Natural Science Foundation of China (Grant No. 11501259).
Funding Information:
K. Matsuzaki: Research supported by Japan Society for the Promotion of Science (KAKENHI 18H01125)
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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.
KW - Asymptotically conformal
KW - Characteristic topological subgroup
KW - Quasisymmetric
KW - Strongly symmetric
KW - Symmetric homeomorphism
KW - VMO
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U2 - 10.1007/s13324-021-00510-7
DO - 10.1007/s13324-021-00510-7
M3 - Article
AN - SCOPUS:85102569122
SN - 1664-2368
VL - 11
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 2
M1 - 79
ER -