A note on the spectral mapping theorem of quantum walk models
  We discuss the description of eigenspace of a quantum walk model $U$ with an associating linear operator $T$ in abstract settings of quantum walk including the Szegedy walk on graphs. In particular, we provide the spectral mapping theorem of $U$ without the spectral decomposition of $T$. Arguments in this direction reveal the eigenspaces of $U$ characterized by the generalized kernels of linear operators given by $T$. 
Kaname Matsue, Osamu Ogurisu and Etsuo Segawa
math-ph math.FA math.MP math.SP quant-ph