This
book contains a self-consistent treatment of Besov spaces for
W*-dynamical systems, based on the Arveson spectrum and Fourier
multipliers. Generalizing classical results by Peller, spaces of Besov
operators are then characterized by trace class properties of the
associated Hankel operators lying in the W*-crossed product algebra.
These criteria allow to extend index theorems to such operator classes.
This in turn is of great relevance for applications in solid-state
physics, in particular, Anderson localized topological insulators as
well as topological semimetals. The book also contains a self-contained
chapter on duality theory for R-actions. It allows to prove a
bulk-boundary correspondence for boundaries with irrational angles which
implies the existence of flat bands of edge states in graphene-like
systems. This book is intended for advanced students in mathematical
physics and researchers alike.