Montel's theorem for real sequence of analytical functions

Question

Let $(f_{n})_{n \in \mathbb{N}}$, $f_{n}: I \longrightarrow D$, ($D \subset \mathbb{R^2}$ a compact set, and $I$ a interval), be a sequence of real analytical functions uniformly bounded. In this case, is Montel's theorem worth? That is, is there a convergent subsequence $(f_{n_{k}})$?

Appreciate.

Answer 1

No. For example, say $f_n(t)=\sin(nt)$.