Title: Spectra of Magnetic Operators on the Diamond Lattice Fractal,
Abstract: We adapt the well-known spectral decimation technique for computing spectra
of Laplacians on certain symmetric self-similar sets to the case of magnetic
Schrodinger operators and work through this method completely for the diamond
lattice fractal. This connects results of physicists from the 1980's, who used
similar techniques to compute spectra of sequences of magnetic operators on
graph approximations to fractals but did not verify existence of a limiting
fractal operator, to recent work describing magnetic operators on fractals via
functional analytic techniques.