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http://dx.doi.org/10.25673/85976
Title: | On a comparison principle and the uniqueness of spectral flow |
Author(s): | Starostka, Maciej Waterstraat, Nils |
Issue Date: | 2022 |
Type: | Article |
Language: | English |
Abstract: | 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. |
URI: | https://opendata.uni-halle.de//handle/1981185920/87929 http://dx.doi.org/10.25673/85976 |
Open Access: | ![]() |
License: | ![]() |
Sponsor/Funder: | Publikationsfonds MLU |
Journal Title: | Mathematische Nachrichten |
Publisher: | Wiley-VCH |
Publisher Place: | [S.l.] |
Volume: | 295 |
Issue: | 4 |
Original Publication: | 10.1002/mana.201900444 |
Page Start: | 785 |
Page End: | 805 |
Appears in Collections: | Open Access Publikationen der MLU |
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Mathematische Nachrichten - 2022 - Starostka - On a comparison principle and the uniqueness of spectral flow.pdf | 247.81 kB | Adobe PDF | ![]() View/Open |