One Consequence of this is that a set eigenfunctions of which is orthogonal at level is also orthogonal at level when extended by spectral decimation.

Since
is a Riemann sum approximation for the integral over the
Sierpinski Gasket of , this relation gives us:

As you can see from the figure:

the correction factor goes to as goes to . (Calculation of the correction factor assumes that subsequent eigenvalues are calculated with unless in which case the first equals .)

Brain Street 2001-11-11