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OverviewThe authors consider a curve of Fredholm pair of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index. As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds. Full Product DetailsAuthor: Bernhelm Booss-Bavnbek , Chaofeng ZhuPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.205kg ISBN: 9781470428006ISBN 10: 1470428008 Pages: 123 Publication Date: 30 April 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsIntroduction Part 1. Maslov index in symplectic Banach spaces: General theory of symplectic analysis in Banach spaces The Maslov index in strong symplectic Hilbert space The Maslov index in Banach bundles over a closed interval Part 2. Applications in global analysis: The desuspension spectral flow formula Appendix A. Perturbation of closed subspaces in Banach spaces Bibliography List of symbols Index of names/authors Subject index Index BibliographyReviewsAuthor InformationBernhelm Booss-Bavnbek, Roskilde University, Denmark. Chaofeng Zhu, Nankai University, Tianjin, People's Republic of China. Tab Content 6Author Website:Countries AvailableAll regions |
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