Inserting a thinspace (\,) between the multiplicative factors should work. Inserting \cdot in these locations should work too. You could also combine the thinspaces with making the outer parentheses a tad bigger than the inner ones (by using \bigl( and \bigr)). The three possibilities are illustrated below:
\documentclass{article} \begin{document} $i(x,y,z,t) = \delta(x-\ell_x(z)) \, \delta(y-\ell_y(z)) \, \hat{\imath}(\xi(z),t)$ $i(x,y,z,t) = \delta(x-\ell_x(z)) \cdot \delta(y-\ell_y(z)) \cdot \hat{\imath}(\xi(z),t)$ $i(x,y,z,t) = \delta\bigl(x-\ell_x(z)\bigr) \, \delta\bigl(y-\ell_y(z)\bigr) \, \hat{\imath}\bigl(\xi(z),t)\bigr)$ \end{document} One can automate the third method by creating a macro such as
\def\myfunc#1{\bigl(#1\bigr)\,} and then typing
$i(x,y,z,t) = \delta\myfunc{x-\ell_x(z)} \delta\myfunc{y-\ell_y(z)} \hat{\imath}\myfunc{\xi(z),t)}$ 
