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Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems de Hermann Schulz-Baldes

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems: Mathematical Physics Studies

Autor Hermann Schulz-Baldes, Tom Stoiber
en Limba Engleză Paperback – 2 ian 2024
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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Specificații

ISBN-13: 9783031122033
ISBN-10: 3031122038
Pagini: 206
Ilustrații: XXIV, 206 p. 7 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.33 kg
Ediția:1st ed. 2022
Editura: Springer International Publishing
Colecția Springer
Seria Mathematical Physics Studies

Locul publicării:Cham, Switzerland

Cuprins

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

Notă biografică

Hermann Schulz-Baldes has been a professor at the Department of Mathematics of the Friedrich-Alexander-University of Erlangen-Nuernberg since 2004. Before this, he received his Ph.D. from the University Paul-Sabatier in Toulouse, and he held several postdoctoral positions in Como, Berlin, and Irvine. His research focuses include the theory of topological insulators, index theory, the study of products of random matrices, and quantum–mechanical scattering theory.
Tom Stoiber is finishing his Ph.D. studies at the Friedrich-Alexander-University of Erlangen-Nuernberg in 2022, with a thesis on non-commutative geometry and its applications in solid-state physics systems. He is supported by a scholarship from the “Studienstiftung des Deutschen Volkes”.

Textul de pe ultima copertă

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.

Caracteristici

Offers a self-contained treatment of harmonic analysis on von Neumann algebras Proves Peller trace class criteria for Hankel operators with Besov symbols Extends index theorems to symbol classes with sufficient Besov regularity