Boundary Value Problems with Global Projection Conditions

Xiaochun Liu

ISBN 10: 3319701134 / ISBN 13: 9783319701134

Published by Birkhäuser, Palgrave Macmillan, 2018

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admitsglobal projection boundary conditions, giving rise to analogues of Toeplitz operators insubspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel's calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.

Seller Inventory # 9783319701134

Bibliographic Details

• Title: Boundary Value Problems with Global Projection Conditions
• Publisher: Birkhäuser, Palgrave Macmillan
• Publication Date: 2018
• Language: English
• ISBN 10: 3319701134
• ISBN 13: 9783319701134
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 29D millimeters 241 millimeters width by 160 millimeters height by 29 millimeters depth
• Weight: 805 grams

About this title

Synopsis

This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel’s calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.