The Maslov index in weak symplectic functional analysis

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Resumé

We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.
OriginalsprogEngelsk
TidsskriftAnnals of Global Analysis and Geometry
Vol/bind44
Udgave nummer3
Sider (fra-til)283-318
Antal sider36
ISSN0232-704X
DOI
StatusUdgivet - okt. 2013

Bibliografisk note

Submitted, 24 July, 2012, Accepted (with suggestions for changes), 28 November 2012, Revised 30 January, 2013, Fully accepted 31 January, 2013

Emneord

  • Closed relations
  • Fredholm pairs of Lagrangians
  • Maslov index
  • Spectral flow
  • Symplectic splitting
  • Weak symplectic structure

Citer dette

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abstract = "We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.",
keywords = "Closed relations, Fredholm pairs of Lagrangians, Maslov index, Spectral flow, Symplectic splitting, Weak symplectic structure, Closed relations, Fredholm pairs of Lagrangians, Maslov index, Spectral flow, Symplectic splitting, Weak symplectic structure",
author = "Bernhelm Booss-Bavnbek and Chaofeng Zhu",
note = "Submitted, 24 July, 2012, Accepted (with suggestions for changes), 28 November 2012, Revised 30 January, 2013, Fully accepted 31 January, 2013",
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The Maslov index in weak symplectic functional analysis. / Booss-Bavnbek, Bernhelm; Zhu, Chaofeng.

I: Annals of Global Analysis and Geometry, Bind 44, Nr. 3, 10.2013, s. 283-318.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - The Maslov index in weak symplectic functional analysis

AU - Booss-Bavnbek, Bernhelm

AU - Zhu, Chaofeng

N1 - Submitted, 24 July, 2012, Accepted (with suggestions for changes), 28 November 2012, Revised 30 January, 2013, Fully accepted 31 January, 2013

PY - 2013/10

Y1 - 2013/10

N2 - We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.

AB - We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.

KW - Closed relations

KW - Fredholm pairs of Lagrangians

KW - Maslov index

KW - Spectral flow

KW - Symplectic splitting

KW - Weak symplectic structure

KW - Closed relations

KW - Fredholm pairs of Lagrangians

KW - Maslov index

KW - Spectral flow

KW - Symplectic splitting

KW - Weak symplectic structure

U2 - 10.1007/s10455-013-9367-z

DO - 10.1007/s10455-013-9367-z

M3 - Journal article

VL - 44

SP - 283

EP - 318

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

SN - 0232-704X

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ER -