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Parabolicity, Volterra Calculus, and Conical Singularities A Volume of Advances in Partial Differential Equations

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 a...

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Bibliographic Details
Other Authors: Albeverio, Sergio (Editor), Demuth, Michael (Editor), Schrohe, Elmar (Editor), Schulze, Bert-Wolfgang (Editor)
Format: eBook
Language:English
Published: Basel Birkhäuser 2002, 2002
Edition:1st ed. 2002
Series:Advances in Partial Differential Equations
Subjects:
Operator Theory
Differential Equations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Volterra Families of Pseudodifferential Operators
  • 1. Basic notation and general conventions
  • 2. General parameter-dependent symbols
  • 3. Parameter-dependent Volterra symbols
  • 4. The calculus of pseudodifferential operators
  • 5. Ellipticity and parabolicity
  • References
  • The Calculus of Volterra Mellin Pseudodifferential Operators with Operator-valued Symbols
  • 1. Preliminaries on function spaces and the Mellin transform
  • 2. The calculus of Volterra symbols
  • 3. The calculus of Volterra Mellin operators
  • 4. Kernel cut-off and Mellin quantization
  • 5. Parabolicity and Volterra parametrices
  • References
  • On the Inverse of Parabolic Systems of Partial Differential Equations of General Form in an Infinite Space-Time Cylinder
  • 1. Preliminary material
  • 2. Abstract Volterra pseudodifferential calculus
  • 3. Parameter-dependent Volterra calculus on a closed manifold
  • 4. Weighted Sobolev spaces
  • 5. Calculi built upon parameter-dependent operators
  • 6. Volterra cone calculus
  • 7. Remarks on the classical theory of parabolic PDE
  • References
  • On the Factorization of Meromorphic Mellin Symbols
  • 1. Introduction
  • 2. Preliminaries
  • 3. Logarithms of pseudodifferential operators
  • 4. The kernel cut-off technique
  • 5. Proof of the main theorem
  • References
  • Coordinate Invariance of the Cone Algebra with Asymptotics
  • 1. Cone operators on the half-axis
  • 2. Operators on higher-dimensional cones
  • References

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