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Boundary Value Problems with Global Projection Conditions: Operator Theory: Advances and Applications, cartea 265

Autor Xiaochun Liu, Bert-Wolfgang Schulze
en Limba Engleză Hardback – 8 noi 2018
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.

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Specificații

ISBN-13: 9783319701134
ISBN-10: 3319701134
Pagini: 400
Ilustrații: XVI, 410 p.
Dimensiuni: 155 x 235 x 26 mm
Greutate: 0.77 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Birkhäuser
Seriile Operator Theory: Advances and Applications, Advances in Partial Differential Equations

Locul publicării:Cham, Switzerland

Cuprins

Introduction.- ​Boundary Value Problems with Global Projection Conditions.- Edge Operators with Global Projection Conditions.- BVPs without the Transmission Property.

Recenzii

“The book is very nice and carefully written, and is a very valuable contribution to the subject … . It is well suited to experts but also to Ph.D. students who are willing to pursue this beautiful and rich area of research.” (Alberto Parmeggiani, Mathematical Reviews, August, 2019)

“The present book is devoted to developing general concepts of ellipticity of boundary value problems (BVPs) and provides a self-contained resource for use by professional researchers.” (David Kapanadze, zbMATH 1423.35003, 2019)

Textul de pe ultima copertă

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.

Caracteristici

Presents the notion of ellipticity with an unification of Shapiro-Lopatinskij elliptic and global projection boundary conditions Discusses spectral boundary conditions for elliptic differential operators Describes Toeplitz-type operators on manifolds with edge, including operators with/without transmission property