Nicolas Essis-Breton
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 Sep 24 revised Show translation is not continuous in $\text{Lip}_\alpha(T)$ state that T is the unit cirlcle Sep 24 comment Show translation is not continuous in $\text{Lip}_\alpha(T)$ @did I want $|x|$ to be the absolute value of x, for example $|-\pi|=\pi$. Then the map $x \mapsto \sqrt{|x|}$ is well-defined on $T$. Sep 24 comment Show translation is not continuous in $\text{Lip}_\alpha(T)$ @DavideGiraudo Yes, $T$ is the unit circle. Sep 24 asked Show translation is not continuous in $\text{Lip}_\alpha(T)$ Sep 23 comment Show with DCT: $\lim_{R \to \infty} \int_0^{2\pi} \frac{id\theta}{\sqrt{1+R^{-2}e^{-2i\theta}}}=\int_0^{2\pi} id\theta$ @did I see your point. How do I get a lower bound for this radius? Sep 23 comment Show with DCT: $\lim_{R \to \infty} \int_0^{2\pi} \frac{id\theta}{\sqrt{1+R^{-2}e^{-2i\theta}}}=\int_0^{2\pi} id\theta$ @did So $\|1+iR^{-1}e{-i\theta}\|^2=1+R^{-2}e^{-2i\theta} \ge 1$, and DCT follows. Is it correct? Sep 23 comment Show with DCT: $\lim_{R \to \infty} \int_0^{2\pi} \frac{id\theta}{\sqrt{1+R^{-2}e^{-2i\theta}}}=\int_0^{2\pi} id\theta$ @did This is the radius of the complex number $1+iR^{-1}e^{-i\theta}$. Sep 23 asked Show with DCT: $\lim_{R \to \infty} \int_0^{2\pi} \frac{id\theta}{\sqrt{1+R^{-2}e^{-2i\theta}}}=\int_0^{2\pi} id\theta$ Sep 16 accepted Does $\int_a^b \text{Im}(f(t))e^{int}dt=0$ implies $f=0$ on $[a,b]$ Sep 16 revised Does $\int_a^b \text{Im}(f(t))e^{int}dt=0$ implies $f=0$ on $[a,b]$ corrected question per Alex Becker comment Sep 16 comment Does $\int_a^b \text{Im}(f(t))e^{int}dt=0$ implies $f=0$ on $[a,b]$ @AlexBecker Good eyes, I meant $\text{Im}(f(t))$ is identically zero. Thank you. Sep 16 asked Does $\int_a^b \text{Im}(f(t))e^{int}dt=0$ implies $f=0$ on $[a,b]$ Sep 16 accepted Does the complex conjugate of an integral equal the integral of the conjugate? Sep 16 asked Does the complex conjugate of an integral equal the integral of the conjugate? Sep 10 awarded Civic Duty Aug 29 accepted Find $\displaystyle{\int_C \left(1+ \frac{2}{z}\right) dz}$ , where $C(\theta)= e^{i\theta}, 0 \le \theta \le \pi$ Aug 28 asked Find $\displaystyle{\int_C \left(1+ \frac{2}{z}\right) dz}$ , where $C(\theta)= e^{i\theta}, 0 \le \theta \le \pi$ Aug 1 awarded Yearling Jun 28 comment Show $g(a)= \operatorname*{arg}_{b \in B} \, f(a,b)=0$ is continuous when $g(a)$ is single-valued and $f$ continuous Our answers are complementary. But You were of precious help and I think you deserve the points. I learn a lot. Thank you. Jun 28 accepted Show $g(a)= \operatorname*{arg}_{b \in B} \, f(a,b)=0$ is continuous when $g(a)$ is single-valued and $f$ continuous