Coverart for item
The Resource Parabolicity, Volterra Calculus, and Conical Singularities : a Volume of Advances in Partial Differential Equations, edited by Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze, (electronic resource)

Parabolicity, Volterra Calculus, and Conical Singularities : a Volume of Advances in Partial Differential Equations, edited by Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze, (electronic resource)

Label
Parabolicity, Volterra Calculus, and Conical Singularities : a Volume of Advances in Partial Differential Equations
Title
Parabolicity, Volterra Calculus, and Conical Singularities
Title remainder
a Volume of Advances in Partial Differential Equations
Statement of responsibility
edited by Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze
Creator
Contributor
Subject
Genre
Language
eng
Summary
This volume highlights the analysis on noncompact and singular manifolds within the framework of the cone calculus with asymptotics. The three papers at the beginning deal with parabolic equations, a topic relevant for many applications. The first article presents a calculus for pseudodifferential operators with an anisotropic analytic parameter. The subsequent paper develops an algebra of Mellin operators on the infinite space-time cylinder. It is shown how timelike infinity can be treated as a conical singularity. In the third text - the central article of this volume - the authors use these results to obtain precise information on the long-time asymptotics of solutions to parabolic equations and to construct inverses within the calculus. There follows a factorization theorem for meromorphic symbols: It is proven that each of these can be decomposed into a holomorphic invertible part and a smoothing part containing all the meromorphic information. It is expected that this result will be important for applications in the analysis of nonlinear hyperbolic equations. The final article addresses the question of the coordinate invariance of the Mellin calculus with asymptotics
Member of
Cataloging source
I9W
http://library.link/vocab/creatorName
Albeverio, Sergio
Dewey number
515.724
Index
no index present
LC call number
QA329-329.9
Literary form
non fiction
Nature of contents
encyclopedias
http://library.link/vocab/relatedWorkOrContributorName
  • Demuth, Michael
  • Schrohe, Elmar
  • Schulze, Bert-Wolfgang
Series statement
Operator Theory: Advances and Applications
Series volume
138
http://library.link/vocab/subjectName
  • Mathematics
  • Operator theory
  • Differential equations, Partial
  • Differential equations, Partial
  • Mathematics
  • Operator theory
Label
Parabolicity, Volterra Calculus, and Conical Singularities : a Volume of Advances in Partial Differential Equations, edited by Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-0348-8191-3
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource (IX, 358 pages).
Form of item
online
Isbn
9783034881913
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-8191-3
Specific material designation
remote
System control number
  • (OCoLC)840290417
  • (OCoLC)ocn840290417
Label
Parabolicity, Volterra Calculus, and Conical Singularities : a Volume of Advances in Partial Differential Equations, edited by Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-0348-8191-3
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource (IX, 358 pages).
Form of item
online
Isbn
9783034881913
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-8191-3
Specific material designation
remote
System control number
  • (OCoLC)840290417
  • (OCoLC)ocn840290417

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