Assume we have a complete orthogonal system (with respect to the L2 norm) on a domain $D$ (for e.g., the set $\{e^{int}\}$ on $[-\pi, \pi]$, or the spherical harmonics on the unit ball). Now consider a domain $D'$, which is "close" to D in some sense (say, the L2 distance between the boundary of $D$ and the boundary of $D'$ is upper bounded). What can be said about the basis of $D'$ ? Is there any sense in which the functions in the basis of $D$ are "close" to the functions in the basis of $D'$ ? Any known results along these or similar lines appreciated.