| Description |
1 online resource (x, 118 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 252, number 1201 |
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Memoirs of the American Mathematical Society ; no. 1201.
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| Contents |
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 |
| Summary |
"We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, we obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions we define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. We 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 |
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As an application, we 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, we 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."--Page v |
| Notes |
"March 2018, volume 252, number 1201 (second of 6 numbers)." |
| Bibliography |
Includes bibliographical references (pages 103-107) and indexes |
| Notes |
Print version record |
| Subject |
Maslov index.
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Symplectic spaces.
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Banach spaces.
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MATHEMATICS -- Geometry -- General.
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Espacios de Banach
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Banach spaces
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Maslov index
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Symplectic spaces
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| Form |
Electronic book
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| Author |
Zhu, Chaofeng, 1973- author.
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American Mathematical Society, publisher
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| ISBN |
1470443716 |
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9781470443719 |
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