Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems / Hermann Schulz-Baldes, Tom Stoiber.
Schulz-Baldes, Hermann, author.; Stoiber, Tom, author.
2022
QC173.458.M38
Available Online

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Title Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems / Hermann Schulz-Baldes, Tom Stoiber.
Author Schulz-Baldes, Hermann, author.
ISBN 9783031122019 (electronic bk.)
3031122011 (electronic bk.)
9783031122002
3031122003
DOI https://doi.org/10.1007/978-3-031-12201-9
Published Cham : Springer, 2022.
Language English
Description 1 online resource (xxiv, 206 pages) : illustrations
Item Number 10.1007/978-3-031-12201-9 doi
Call Number QC173.458.M38
Dewey Decimal Classification 530.410151
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Stoiber, Tom, author.
Series Mathematical physics studies, 2352-3905
Available in Other Form HARMONIC ANALYSIS ON OPERATOR ALGEBRAS AND ITS APPLICATIONS TO INDEX THEORY.
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Preliminaries on Crossed Products
Besov Spaces for Isometric G-actions
Quantum Differentiation and Index Theorems
Duality for Toeplitz Extensions
Applications to Solid State Systems.

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