Pseudo-Differential Operators on Manifolds with Singularities

Pseudo-Differential Operators on Manifolds with Singularities

1st Edition - October 17, 1991

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  • Author: B.-W. Schulze
  • eBook ISBN: 9780080875453

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The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics.The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

Table of Contents

  • The Conormal Asymptotics on R+. The Mellin Transform. Spaces with Conormal Asymptotics. The Mellin Expansion of Operators. Operators on Manifolds with Conical Singularities. Spaces with Conormal Asymptotics for the Cone. The Mellin Expansions for the Cone. The Parameter-Dependent Cone Calculus. Operators on Manifolds with Edges. Preliminary Constructions. Pseudo-Differential Operators with Operator-Valued Symbols. Pseudo-Differential Operators on Manifolds with Edges. References. Index.

Product details

  • No. of pages: 409
  • Language: English
  • Copyright: © North Holland 1991
  • Published: October 17, 1991
  • Imprint: North Holland
  • eBook ISBN: 9780080875453

About the Author

B.-W. Schulze

Affiliations and Expertise

Karl-Weierstrass-Institut für Mathematik, Berlin, Germany

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