Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems (Mathematical Physics Studies)
Schulz-Baldes, Hermann; Stoiber, Tom
ISBN 10: 3031122003 ISBN 13: 9783031122002
Verlag: Springer, 2023
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In. Bestandsnummer des Verkäufers ria9783031122002_new
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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.
Über die Autorin bzw. den Autor:
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”.
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Titel: Harmonic Analysis in Operator Algebras and ...
Verlag: Springer
Erscheinungsdatum: 2023
Einband: Hardcover
Zustand: New
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Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems
Verlag:
Springer International Publishing, 2023
ISBN 10: 3031122003
ISBN 13: 9783031122002
Neu
Hardcover
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 forR-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. Artikel-Nr. 9783031122002
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