What is the transfer function of an ideal buffer in time domain?
You can say that the impulse response of an ideal buffer is a Dirac pulse. Which is actually quite obvious, because the impulse response has to return the impulse response again in its entirety.

Other variations on the matter:

$$\begin{align}
y(t) &amp;= u(t)\\
&amp;\Updownarrow \mathcal{L}\{\}\\
Y(s) &amp;= U(s)\\
&amp;\Downarrow\\
G(s) &amp;= \frac{Y(s)}{U(s)}=1
\end{align}$$

If you want to express this linear function in the time domain, then you would indeed get

$$\begin{align}
G(s) &amp;= 1\\
&amp;\Updownarrow \mathcal{L}^{-1}\{\}\\
g(t) &amp;= \delta(t)
\end{align}$$

Which has the property:

$$f(t) * g(t) = f(t)$$