  The spectra of parallel flows (that is, flows governed by first-order
differential operators parallel to one direction) are investigated, on both
$L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow
admitting a purely singular continuous spectrum is provided. For flows
admitting more regular spectra the density of states is analyzed, and spaces on
which it is uniformly bounded are identified. As an application, an ergodic
theorem with uniform convergence is proved.

Spectral Theory;Functional Analysis