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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.
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