Hermann Schulz-Baldes,Tom Stoiber
Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems
Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems
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- More about Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems
This book provides a comprehensive treatment of Besov spaces for W*-dynamical systems,characterizing them through trace class properties of Hankel operators and extending index theorems to operator classes. It also discusses duality theory for R-actions,implying the existence of flat bands of edge states in graphene-like systems.
Format: Hardback
Length: 206 pages
Publication date: 01 January 2023
Publisher: Springer International Publishing AG
This comprehensive text offers a thorough exploration of Besov spaces for W*-dynamical systems, drawing upon the Arveson spectrum and Fourier multipliers. By extending classical results by Peller, it characterizes spaces of Besov operators through trace class properties of their associated Hankel operators in the W*-crossed product algebra. This extension enables the application of index theorems to these operator classes, holding significant importance for applications in solid-state physics. In particular, it sheds light on Anderson localized topological insulators and topological semimetals. Additionally, the book includes a self-contained chapter on duality theory for R-actions, which establishes a bulk-boundary correspondence for boundaries with irrational angles. This correspondence implies the existence of flat bands of edge states in graphene-like systems. Designed for advanced students in mathematical physics and researchers, this text provides a deep understanding of the subject matter.
Weight: 518g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031122002
Edition number: 1st ed. 2022
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