On a comparison principle and the uniqueness of spectral flow

Starostka Maciej; Waterstraat Nils

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On a comparison principle and the uniqueness of spectral flow

机译：On a comparison principle and the uniqueness of spectral flow

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The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply our result to the existence of non-trivial solutions of boundary value problems of Hamiltonian systems. Secondly, the spectral flow was axiomatically characterised by Lesch, and by Ciriza, Fitzpatrick and Pejsachowicz under the assumption that the endpoints of the paths of selfadjoint Fredholm operators are invertible. We propose a different approach to the uniqueness of spectral flow which lifts this additional assumption. As application of the latter result, we discuss the relation between the spectral flow and the Maslov index in symplectic Hilbert spaces.

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《Mathematische Nachrichten》 |2022年第4期|785-805|共21页
作者
Starostka Maciej; Waterstraat Nils;
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作者单位

Gdansk Univ Technol;

Martin Luther Univ Halle Wittenberg;

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原文格式 PDF
正文语种英语
中图分类数学;
关键词
Hamiltonian systems; Maslov Index; spectral flow; symplectic Hilbert spaces; FREDHOLM OPERATORS; CRITICAL-POINTS; BIFURCATION; FUNCTIONALS;

On a comparison principle and the uniqueness of spectral flow

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