Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems

Schulz-Baldes, Hermann; Stoiber, Tom

ISBN 10: 303112202X ISBN 13: 9783031122026

Editorial: Springer, 2023

Idioma: Ingl�s

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T�tulo

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems

Editor

Springer

Fecha de publicaci�n

2023

Idioma

Ingl�s

ISBN 10

303112202X

ISBN 13

9783031122026

Encuadernaci�n

Encuadernaci�n de tapa blanda

Estado

New

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Sinopsis

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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