Open Access
An intrinsic definition of the Colombeau generalized functions
Jiří Jelínek
- Vol. 40, Iss: 1, pp 71-95
Reads0
Chats0
TLDR
In this article, a modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the spaces of the generalized functions on a C∞ manifold.Abstract:
A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a C∞ manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.read more
Citations
More filters
Journal ArticleDOI
The use of generalized functions and distributions in general relativity
TL;DR: In this paper, a mathematical theory of nonlinear generalized functions based on Colombeau algebras is described and applied in general relativity, and it is shown that certain solutions with weak singularities may be regarded as distributional solutions of Einstein's equations.
Posted Content
On the foundations of nonlinear generalized functions I
TL;DR: In this article, a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz is constructed.
Journal ArticleDOI
A Global Theory of Algebras of Generalized Functions
TL;DR: In this article, a geometric approach to define an algebra G (M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space D ∞(M) of distributions on M. This algebra is a differential algebra, its elements possessing Lie derivatives with respect to arbitrary smooth vector fields.
Journal ArticleDOI
The use of Generalised Functions and Distributions in General Relativity
TL;DR: In this article, the authors review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations and show that there are some physically interesting cases which cannot be treated using distribution theory but require a more general concept.
Posted Content
A global theory of algebras of generalized functions
TL;DR: In this paper, the Colombeau algebra of generalized functions on a smooth manifold was defined and a canonical linear embedding of the distribution space of the distributions on the manifold was constructed.
References
More filters
Book
Théorie des distributions
TL;DR: The merite as discussed by the authors is a date marque une date dans le progres des mathematiques and de la physique en levant l'ambiguite que constituait le succes des methodes de calcul symbolique aupres des physiciens and l'inacceptabilite de leurs formules au regard de la rigueur mathematiques.
Book
The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis
Lars Hörmander,L. Hörmander +1 more
Book
Elementary introduction to new generalized functions
TL;DR: In this article, the author's previous book ''New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced ''new generalized functions'' in order to explain heuristic computations of physics and to give a meaning to any finite product of distributions.