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The purpose of this publication is to present, in one book, various approaches to analytic problems that arise in the context of singular spaces. It is based on the workshop 'Approaches to Singular Analysis' which was held on April 8-10, 1999, at Humboldt University of Berlin. The aim of this workshop was to bring together young mathematicians interested in partial differential operators on singular con figurations. The main idea was to look at different approaches that have been proposed, and try to understand to which extent they overlap and how they differ. The workshop took place in a rather relaxed atmosphere. The participants appreciated that there was a discussion session every day, which gave a lot of room for an open exchange of ideas. This book contains articles by workshop participants and invited contributions. The former are expanded versions of talks at the workshop; they give introductions to various pseudodifferential calculi and discussions of relations between them. In addition, we invited a limited number of papers from mathematicians who have made significant contributions to this field. Unfortunately, several of these invita tions were turned down due to other commitments. For this reason, only a very small number of contributions from non-participants remain. The absence of any particular name from the list of (invited) contributors should not be interpreted as a bias of the editors against that scientist. It rather reflects our restricted choice of invitations due to lack of space.
List of contents
The Cone Algebra and a Kernel Characterization of Green Operators.- Basics of the b-Calculus.- A Short Introduction to Boutet de Monvel's Calculus.- Singular Asymptotics Lemma and Push-Forward Theorem.- Pseudodifferential Analysis on Manifolds with Boundary - a Comparison of b-Calculus and Cone Algebra.- Operator Algebras with Symbol Hierarchies on Manifolds with Singularities.- The Resolvent Expansion on Singular Spaces.- A General Index Formula on Toric Manifolds with Conical Points.
About the author
Prof. Dr. Daniel Grieser lehrt und forscht am Institut für Mathematik der Carl von Ossietzky Universität Oldenburg.
Summary
The purpose of this publication is to present, in one book, various approaches to analytic problems that arise in the context of singular spaces. It is based on the workshop 'Approaches to Singular Analysis' which was held on April 8-10, 1999, at Humboldt University of Berlin. The aim of this workshop was to bring together young mathematicians interested in partial differential operators on singular con figurations. The main idea was to look at different approaches that have been proposed, and try to understand to which extent they overlap and how they differ. The workshop took place in a rather relaxed atmosphere. The participants appreciated that there was a discussion session every day, which gave a lot of room for an open exchange of ideas. This book contains articles by workshop participants and invited contributions. The former are expanded versions of talks at the workshop; they give introductions to various pseudodifferential calculi and discussions of relations between them. In addition, we invited a limited number of papers from mathematicians who have made significant contributions to this field. Unfortunately, several of these invita tions were turned down due to other commitments. For this reason, only a very small number of contributions from non-participants remain. The absence of any particular name from the list of (invited) contributors should not be interpreted as a bias of the editors against that scientist. It rather reflects our restricted choice of invitations due to lack of space.
