Spectral Flow : A Functional Analytic and Index-Theoretic Approach

Doll, Nora; Schulz-Baldes, Hermann; Waterstraat, Nils

doi:10.1515/9783111172477

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https://library.oapen.org/bitstream/20.500.12657/63798/1/9783111172477.pdf
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https://library.oapen.org/bitstream/20.500.12657/63798/1/9783111172477.pdf

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://directory.doabooks.org/handle/20.500.12854/101580

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