Title | Parabolicity, Volterra Calculus, and Conical Singularities [electronic resource] : A Volume of Advances in Partial Differential Equations / edited by Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8191-3 |
Descript | XI, 359 p. online resource |
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