  We consider solutions to the linear wave equation on a suitable globally
hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from
regular initial data prescribed on a Cauchy hypersurface crossing the future
event horizon. We obtain boundedness, decay, non-decay and blow-up results. Our
estimates hold up to and including the event horizon. The fundamental new
aspect of this problem is the degeneracy of the redshift on the event horizon.
Several new analytical features of degenerate horizons are also presented.
