example, holomorphic function on unit disc with radial limits everywhere zero

Question

I tried to look for examples of a non zero holomorphic function $f : \mathbb{D} \to \mathbb{C} $ such that, $\forall\xi \in \partial \mathbb{D}$ $$\lim_{r\to1^{-}} f (r\xi)=0, $$

So, could anyone demonstrate examples of such functions. Moreover, what properties should, such a function have? In other worlds are there any sufficient and/ or necessary conditions?

Finally, the topic of boundary behavior of holomorphic functions is seems really chaotic. Is there are any reference with examples of the various behaviors holomorphic functions exhibit in their boundary?

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edit I added a image of the notes I am reading witch triggered the question. So the writer implies that such a function exists.. unless I miss something..