eBook ISBN:  9781470443719 
Product Code:  MEMO/252/1201.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 
eBook ISBN:  9781470443719 
Product Code:  MEMO/252/1201.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 252; 2018; 123 ppMSC: Primary 53; Secondary 58
The authors consider a curve of Fredholm pairs 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 finitedimensional 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 wellposed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

Table of Contents

Chapters

Preface

Introduction

1. Maslov index in symplectic Banach spaces

1. General theory of symplectic analysis in Banach spaces

2. The Maslov index in strong symplectic Hilbert space

3. The Maslov index in Banach bundles over a closed interval

2. Applications in global analysis

4. The desuspension spectral flow formula

A. Perturbation of closed subspaces in Banach spaces


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The authors consider a curve of Fredholm pairs 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 finitedimensional 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 wellposed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

Chapters

Preface

Introduction

1. Maslov index in symplectic Banach spaces

1. General theory of symplectic analysis in Banach spaces

2. The Maslov index in strong symplectic Hilbert space

3. The Maslov index in Banach bundles over a closed interval

2. Applications in global analysis

4. The desuspension spectral flow formula

A. Perturbation of closed subspaces in Banach spaces