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 Jul 17 awarded Yearling Apr 16 awarded Nice Question Dec 3 awarded Popular Question Sep 24 awarded Autobiographer Jul 2 awarded Curious Apr 23 comment Linear Fractional Transforms maps the upper half unit disc onto the first quadrant @LeeMosher: I feel ashamed for asking this question. I should read my textbook more carefully. The point here is that LFT preserve angles on the whole complex plane except one possible point. The upper half disc has two right angles on the boundary, then one of them must be map to the origin. Say, $z=-1$, then $z=1$ must be map to $\infty$, and then the LFT is not analytic at $z=1$. So, there is no such an "angle preserving" at $z=1$. And hence my question does not make sense. I hope I get the point. Apr 18 comment Linear Fractional Transforms maps the upper half unit disc onto the first quadrant @LeeMosher:I think there are two such LFTs, $T(z)=k(1+z)/(1-z),k>0$ and $T(z)=ih(1-z)/(1+z),h>0$. If you wanna me choose one, I wanna say: Both. ：） Apr 18 asked Linear Fractional Transforms maps the upper half unit disc onto the first quadrant Apr 17 accepted Continuous piecewise smooth function $=$ a globally $\mathcal{C}^1$ function $+\sum a_i|s-\alpha_i|$? Apr 15 answered Continuous piecewise smooth function $=$ a globally $\mathcal{C}^1$ function $+\sum a_i|s-\alpha_i|$? Apr 15 awarded Informed Apr 14 asked Continuous piecewise smooth function $=$ a globally $\mathcal{C}^1$ function $+\sum a_i|s-\alpha_i|$? Apr 14 accepted An inequality of J. Necas Nov 8 awarded Yearling Oct 17 accepted About the trace of Sobolev functions Oct 16 revised About the trace of Sobolev functions added 49 characters in body Oct 16 comment About the trace of Sobolev functions @Jose27:Sorry,$W^{1-1/p,p}(\partial\Omega)$ is defined as the image of $W^{1,p}(\Omega)$. Oct 16 comment About the trace of Sobolev functions @Jose27:Thanks, I added this in my question. Oct 16 revised About the trace of Sobolev functions added 78 characters in body Oct 16 comment About the trace of Sobolev functions @Tomás:Corrected,thanks!