The 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.
Les mer
The 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.
Les mer
IntroductionPart 1. Maslov index in symplectic Banach spaces: General theory of symplectic analysis in Banach spacesThe Maslov index in strong symplectic Hilbert spaceThe Maslov index in Banach bundles over a closed intervalPart 2. Applications in global analysis: The desuspension spectral flow formulaAppendix A. Perturbation of closed subspaces in Banach spacesBibliographyList of symbolsIndex of names/authorsSubject indexIndexBibliography
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Produktdetaljer

ISBN
9781470428006
Publisert
2018-04-30
Utgiver
Vendor
American Mathematical Society
Vekt
205 gr
Høyde
254 mm
Bredde
178 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
123

Biographical note

Bernhelm Booss-Bavnbek, Roskilde University, Denmark.

Chaofeng Zhu, Nankai University, Tianjin, People's Republic of China.