Spectral Flow

A Functional Analytic and Index-Theoretic Approach

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Author(s)
Doll, Nora
Schulz-Baldes, Hermann
Waterstraat, Nils
Language
English
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Abstract
This is the first treatment entirely dedicated to an analytic study of spectral flow for paths of selfadjoint Fredholm operators, possibly unbounded or understood in a semi finite sense. The importance of spectral flow for homotopy and index theory are discussed in detail. Applications concern eta-invariants, the Bott-Maslov and Conley-Zehnder indices, Sturm-Liouville oscillation theory, the spectral localizer and bifurcation theory.
URI
https://doab-dev.siscern.org/handle/20.500.12854/170739
Keywords
Self-adjoint Fredholm operators; topologies; thereon Index; theory of Fredholm pairs; Bott-Maslov and Conley-Zehnder indices; Oscillation theory Jacobi operators; scattering theory; Variational bifurcation theory; thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations; thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis; thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics
DOI
10.1515/9783111172477
ISBN
9783111172477, 9783111169897, 9783111173085
Publisher
De Gruyter
Publisher website
http://www.degruyter.com/
Publication date and place
Berlin/Boston, 2023
Imprint
De Gruyter
Series
De Gruyter Studies in Mathematics,
Pages
442