Aspects of Boundary Problems in Analysis and Geometry [electronic resource]

Aspects of Boundary Problems in Analysis and Geometry
Author: Juan Gil, Thomas Krainer, Ingo Witt
Published by Birkhäuser Basel
ISBN: 978-3-0348-9595-8
DOI: 10.1007/978-3-0348-7850-0

Table of Contents:

• Spectral invariants of operators of Dirac type on partitioned manifolds
• Index theory of Dirac operators on manifolds with corners up to codimension two
• Index defects in the theory of spectral boundary value problems
• Cyclic homology and pseudodifferential operators, a survey
• Index and secondary index theory for flat bundles with duality
• Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
• On the tangential oblique derivative problem — methods, results, open problems
• A note on boundary value problems on manifolds with cylindrical ends
• Relative elliptic Theory

Preface -- I. Geometric Operators and the Index - Contributions by D. Bleecker and B. Booss-Bavnbek, P. Loya, A. Savin and B. Sternin, M.-T. Benameur, J. Brodzki and V. Nistor, U. Bunke and X. Ma -- II. Elliptic Boundary Value Problems - Contributions by B.-W. Schulze, P. Popivanov, M. Mitrea and V. Nistor, V. Nazaikinskii and B. Sternin
Boundary problems constitute an essential field of common mathematical interest. The intention of this volume is to highlight several analytic and geometric aspects of boundary problems with special emphasis on their interplay. It includes surveys on classical topics presented from a modern perspective as well as reports on current research. The collection splits into two related groups: - analysis and geometry of geometric operators and their index theory - elliptic theory of boundary value problems and the Shapiro-Lopatinsky condition