We consider the space $E$ of continuous functions from $[0,1]$ to $\mathbb{R}$, equipped with the inner product defined by
$$\langle f, g \rangle = \int_0^1 f(t) g(t)\,\mathrm{d}t$$
Show that $(E, \langle \cdot, \cdot \rangle)$ is not a reproducing kernel Hilbert space.