We investigate in greater detail a sampling formula given by the first
author for functions whose spectrum lies in a Cantor set $K$ of
a special type introduced by Jorgensen and Pedersen, where the sampling
set is extremely thin, and the sampling function is quite
different from the usual sinc function. We obtain new properties
of the sampling function, and we give approximate descriptions of both
local and global behavior of functions with spectrum in $K$. Some
experimental results are described, and more can be found at
http://mathlab.cit.cornell.edu/tillman.