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**Dinkydoe** Let f be a continuous function on $\displaystyle D=\left\{z:|z|=1\right\}$. Laat $\displaystyle \gamma:[0,2\pi]\to D$, defined by $\displaystyle \gamma(t)=e^{it}$.

Define the function $\displaystyle F$ as follows:

$\displaystyle F(z) = f(z)$ if $\displaystyle |z|=1$

$\displaystyle F(z) = \frac{1}{2\pi i}\int_\gamma \frac{f(\zeta)}{\zeta-z}d\zeta$ if $\displaystyle |z|< 1$

Is $\displaystyle F$ continuous on $\displaystyle \overline{D}(0,1)$ [Hint:Consider $\displaystyle f(z)=\overline{z}$]

How would one go to tackle this problem?