# Regarding continuous function not in the Disc algebra

Let $$D=\{z\in\mathbb{C}: |z|<1\}$$.

$$C(\bar{D})=\{f:\bar D\longrightarrow \mathbb{C}: f \;\text{is continuous on}\; \bar{D}\}$$

$$A(D)=\{f\in C(\bar{D}): f \;\text{is analytic in} \;D\}$$ Can you give me example of a function which is in $$C(\bar{D})$$ but not in $$A(D)$$? A function that is not analytic exactly at the boundary but continuous.

• How about $z\mapsto\overline{z}$? – SmileyCraft Jan 10 at 16:03

Any function that is not differentiable will do. For instance $$f(z)=|z|$$.