quasisymmetric homeomorphisms
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2020 ◽  
Vol 45 (1) ◽  
pp. 53-66
Author(s):  
Shuan Tang ◽  
Pengcheng Wu

2018 ◽  
Vol 64 (7) ◽  
pp. 1184-1199
Author(s):  
Tao Cheng ◽  
Shanshuang Yang

2017 ◽  
Vol 42 ◽  
pp. 921-930 ◽  
Author(s):  
Yue Fan ◽  
Yun Hu ◽  
Yuliang Shen

2016 ◽  
Vol 23 (4) ◽  
pp. 615-622 ◽  
Author(s):  
Armen Sergeev

AbstractIn this paper, we give an interpretation of some classical objects of function theory in terms of Banach algebras of linear operators in a Hilbert space. We are especially interested in quasisymmetric homeomorphisms of the circle. They are boundary values of quasiconformal homeomorphisms of the disk and form a group ${\operatorname{QS}(S^{1})}$ with respect to composition. This group acts on the Sobolev space ${H^{1/2}_{0}(S^{1},\mathbb{R})}$ of half-differentiable functions on the circle by reparameterization. We give an interpretation of the group ${\operatorname{QS}(S^{1})}$ and the space ${H^{1/2}_{0}(S^{1},\mathbb{R})}$ in terms of noncommutative geometry.


2011 ◽  
Vol 191 (1) ◽  
pp. 209-226 ◽  
Author(s):  
Yun Hu ◽  
Yuliang Shen

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