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Parabolicity, Volterra Calculus, and Conical Singularities

A Volume of Advances in Partial Differential Equations

  • Book
  • © 2002

Overview

Editors:
  1. Sergio Albeverio

    1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

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  2. Michael Demuth

    1. Institut für Mathematik, Technische Universität Clausthal, Clausthal-Zellerfeld, Germany

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  3. Elmar Schrohe

    1. Institut für Mathematik, Universität Potsdam, Potsdam, Germany

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  4. Bert-Wolfgang Schulze

    1. Institut für Mathematik, Universität Potsdam, Potsdam, Germany

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 138)

Part of the book sub series: Advances in Partial Differential Equations (APDE)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
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  2. Volterra Families of Pseudodifferential Operators

    • Thomas Krainer
    Pages 1-45

  3. The Calculus of Volterra Mellin Pseudodifferential Operators with Operator-valued Symbols

    • Thomas Krainer
    Pages 47-91

  4. On the Inverse of Parabolic Systems of Partial Differential Equations of General Form in an Infinite Space-Time Cylinder

    • Thomas Krainer, Bert-Wolfgang Schulze
    Pages 93-278

  5. On the Factorization of Meromorphic Mellin Symbols

    • Ingo Witt
    Pages 279-306

  6. Coordinate Invariance of the Cone Algebra with Asymptotics

    • D. Kapanadze, B.-W. Schulze, I. Witt
    Pages 307-358
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Keywords

About this book

Partial differential equations constitute an integral part of mathematics. They lie at the interface of areas as diverse as differential geometry, functional analysis, or the theory of Lie groups and have numerous applications in the applied sciences. A wealth of methods has been devised for their analysis. Over the past decades, operator algebras in connection with ideas and structures from geometry, topology, and theoretical physics have contributed a large variety of particularly useful tools. One typical example is the analysis on singular configurations, where elliptic equations have been studied successfully within the framework of operator algebras with symbolic structures adapted to the geometry of the underlying space. More recently, these techniques have proven to be useful also for studying parabolic and hyperbolic equations. Moreover, it turned out that many seemingly smooth, noncompact situations can be handled with the ideas from singular analysis. The three papers at the beginning of this volume highlight this aspect. They deal with parabolic equations, a topic relevant for many applications. The first article prepares the ground by presenting a calculus for pseudo differential operators with an anisotropic analytic parameter. In the subsequent paper, an algebra of Mellin operators on the infinite space-time cylinder is constructed. It is shown how timelike infinity can be treated as a conical singularity.

Editors and Affiliations

  • Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Sergio Albeverio

  • Institut für Mathematik, Technische Universität Clausthal, Clausthal-Zellerfeld, Germany

    Michael Demuth

  • Institut für Mathematik, Universität Potsdam, Potsdam, Germany

    Elmar Schrohe, Bert-Wolfgang Schulze

Bibliographic Information

  • Book Title: Parabolicity, Volterra Calculus, and Conical Singularities

  • Book Subtitle: A Volume of Advances in Partial Differential Equations

  • Editors: Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8191-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2002

  • Hardcover ISBN: 978-3-7643-6906-4Published: 21 November 2002

  • Softcover ISBN: 978-3-0348-9469-2Published: 13 October 2012

  • eBook ISBN: 978-3-0348-8191-3Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XI, 359

  • Topics: Operator Theory, Partial Differential Equations

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