A Theory Of Differentiation In Locally Convex Spaces
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A Theory of Differentiation in Locally Convex Spaces
Author: Sadayuki Yamamuro
language: en
Publisher: American Mathematical Soc.
Release Date: 1979
A theory of differentiation is constructed on locally convex spaces based on the correspondence between the sets of semi-norms which induce original topologies.
On the Foundations of Nonlinear Generalized Functions I and II
Author: Michael Grosser
language: en
Publisher: American Mathematical Soc.
Release Date: 2001
In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.
Geometric Theory of Generalized Functions with Applications to General Relativity
Author: M. Grosser
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.