Parabolicity, Volterra Calculus, and Conical Singularities

Beschreibung:

Editor(s): Albeverio, Sergio; Demuth, Michael; Schrohe, Elmar; Schulze, Bert-Wolfgang. Series: Operator Theory: Advances and Applications / Advances in Partial Differential Equations. Num Pages: 370 pages, biography. BIC Classification: PBKA; WM. Category: (G) General (US: Trade). Dimension: 235 x 155 x 19. Weight in Grams: 575. . 2002. Softcover reprint of the original 1st ed. 2002. Paperback. . . . . Books ship from the US and Ireland. Bestandsnummer des Verkäufers V9783034894692

Diesen Artikel melden

Inhaltsangabe:

Reseña del editor: 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.