Schulz-Baldes H, Stoiber T (2022)

**Publication Language:** English

**Publication Type:** Authored book

**Publication year:** 2022

**Publisher:** Springer

**Series:** Mathematical Physics Studies

**City/Town:** Cham

**DOI:** 10.1007/978-3-031-12201-9

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.

Hermann Schulz-Baldes
Professur für Mathematik (Mathematische Physik)
Tom Stoiber
Professur für Mathematik (Mathematische Physik)

**APA:**

Schulz-Baldes, H., & Stoiber, T. (2022). *Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems. *Cham: Springer.

**MLA:**

Schulz-Baldes, Hermann, and Tom Stoiber. *Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems.* Cham: Springer, 2022.

**BibTeX:** Download