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Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems/ by Hermann Schulz-Baldes, Tom Stoiber.
Author:	Schulz-Baldes, Hermann.
other author:	Stoiber, Tom.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xxiv, 206 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Condensed matter - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-031-12201-9
ISBN:	9783031122019

Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems
Schulz-Baldes, Hermann.

Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems[electronic resource] /by Hermann Schulz-Baldes, Tom Stoiber. - Cham :Springer International Publishing :2022. - xxiv, 206 p. :ill., digital ;24 cm. - Mathematical physics studies,2352-3905. - Mathematical physics studies..

Preliminaries on Crossed Products -- Besov Spaces for Isometric G-actions -- Quantum Differentiation and Index Theorems -- Duality for Toeplitz Extensions -- Applications to Solid State Systems.

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.

ISBN: 9783031122019

Standard No.: 10.1007/978-3-031-12201-9doiSubjects--Topical Terms:

1408346
Condensed matter
--Mathematics.

LC Class. No.: QC173.458.M38

Dewey Class. No.: 530.410151

Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems
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245 1 0 $a Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems $h [electronic resource] / $c by Hermann Schulz-Baldes, Tom Stoiber.
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300 $a xxiv, 206 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematical physics studies, $x 2352-3905
505 0 $a Preliminaries on Crossed Products -- Besov Spaces for Isometric G-actions -- Quantum Differentiation and Index Theorems -- Duality for Toeplitz Extensions -- Applications to Solid State Systems.
520 $a 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.
650 0 $a Condensed matter $x Mathematics. $3 1408346
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650 0 $a Besov spaces. $3 1210597
700 1 $a Stoiber, Tom. $3 1408345
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