That is to say, the domain of the closure has the same boundary conditions as the domain of "A" itself, just a less stringent smoothness assumption. Meanwhile, since there are "too many" boundary conditions on "A", there are "too few" (actually, none at all in this case) for formula_6. If we compute formula_66 for formula_67 using integration by parts, then since formula_68 vanishes at both ends of the interval, no boundary conditions on formula_69 are needed to cancel out the boundary terms in the integration by parts. Thus, any sufficiently smooth function formula_69 is in the domain of formula_6, with formula_72.