  For certain elliptic differential operators $L,$ we study the behaviour of
solutions to $Lu=0,$ as we tend to the boundary along radii in strictly
starlike domains in $\R^n, n\ge 3.$ Analogous results are obtained in other
special domains. Our approach involves introducing harmonic line bundles as
instances of Brelot harmonic spaces and approximating continuous functions by
harmonic functions on appropriate subsets. These approximation theorems on
harmonic spaces yield interesting examples for approximation by solutions of
$Lu=0$ on some domains in $\R^n.$
