Overview
- 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
Part of the book series: Mathematical Physics Studies (MPST)
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Table of contents (5 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the authors
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”.
Bibliographic Information
Book Title: Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems
Authors: Hermann Schulz-Baldes, Tom Stoiber
Series Title: Mathematical Physics Studies
DOI: https://doi.org/10.1007/978-3-031-12201-9
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-12200-2Published: 01 January 2023
Softcover ISBN: 978-3-031-12203-3Published: 02 January 2024
eBook ISBN: 978-3-031-12201-9Published: 31 December 2022
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 1
Number of Pages: XXIV, 206
Number of Illustrations: 7 b/w illustrations
Topics: Condensed Matter Physics, Algebra, Group Theory and Generalizations, K-Theory