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

Tom Stoiber

ISBN 10: 3031122003 / ISBN 13: 9783031122002

Editore: Springer, 2023

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems In deutscher Sprache. pages. Codice articolo BN401670

Riassunto:

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.

Informazioni sull'autore:

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”.

Dati bibliografici

Titolo: Harmonic Analysis in Operator Algebras and ...
Casa editrice: Springer
Data di pubblicazione: 2023
Legatura: Hardcover
Condizione: gut
Edizione: 2023.