It seems from Rudin's functional analysis (P168, Thm6.27), the Dirac distribution $\delta_0$ on $R^1$ can be written as $$ \delta_0=f_0+f'_1+f''_2, $$ for $\{f_i\}_{i=0}^2\in C(R^1)$, there $'$ should be understand as derivative of distruibution of course.
My problem is, can we write down $f_i$ exactly?
The Dirac distribution is defined as $$ \delta_0(\phi)=\phi(0),\quad\phi\in C_0^\infty(R) $$