© 2002

Parabolicity, Volterra Calculus, and Conical Singularities

A Volume of Advances in Partial Differential Equations

  • Sergio Albeverio
  • Michael Demuth
  • Elmar Schrohe
  • Bert-Wolfgang Schulze

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

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.


Pseudodifferential operators calculus differential equation hyperbolic equation partial differential equation partial differential equations

Editors and affiliations

  • Sergio Albeverio
    • 1
  • Michael Demuth
    • 2
  • Elmar Schrohe
    • 3
  • Bert-Wolfgang Schulze
    • 3
  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany
  2. 2.Institut für MathematikTechnische Universität ClausthalClausthal-ZellerfeldGermany
  3. 3.Institut für MathematikUniversität PotsdamPotsdamGermany

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
  • Copyright Information Birkhäuser Verlag 2002
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-6906-4
  • Softcover ISBN 978-3-0348-9469-2
  • eBook ISBN 978-3-0348-8191-3
  • Edition Number 1
  • Number of Pages XI, 359
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
    Partial Differential Equations
  • Buy this book on publisher's site