On a formula for the spectral flow and its applications |
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| Authors: | Pierluigi Benevieri Paolo Piccione |
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| Institution: | 1. Dipartimento di Matematica Applicata, Universit?degli Studi di Firenze, Via S. Marta 3, 50139 Firenze, Italy;2. Departamento de Matem?tica, Universidade de S?o Paulo, Rua do Mat?o 1010, CEP 05508‐900, S?o Paulo, SP, Brazil |
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| Abstract: | We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi‐Riemannian geodesic, and we compute its value in terms of the Maslov index (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Fredholm operators spectral flow periodic geodesic semi‐Riemannian manifolds Maslov index |
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