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Book Cover
Author Albeverio, Sergio.

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.

Published Basel : Birkh衵ser Basel : Imprint : Birkh衵ser, 2002.


Location Call No. Status
Physical description 1 online resource (IX, 358 pages).
Series Operator Theory: Advances and Applications ; 138
Operator theory, advances and applications ; 138.
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.
Other author Demuth, Michael.
Schrohe, Elmar.
Schulze, Bert-Wolfgang.
Subject Mathematics.
Operator theory.
Differential equations, Partial.
Differential equations, Partial.
Operator theory.
Electronic books.
ISBN 9783034881913 (electronic bk.)
3034881916 (electronic bk.)