[LIVRE][B] Geometric theory of generalized functions with applications to general relativity

M Grosser, M Kunzinger, M Oberguggenberger… - 2013 - books.google.com
Over the past few years a certain shift of focus within the theory of algebras of generalized
functions (in the sense of JF Colombeau) has taken place. Originating in infinite dimensional …

[LIVRE][B] Linear theory of Colombeau generalized functions

M Nedeljkov, S Pilipovic, D Scarpalézos - 1998 - books.google.com
Results from the now-classical distribution theory involving convolution and Fourier
transformation are extended to cater for Colombeau's generalized functions. Indications are …

[LIVRE][B] On the foundations of nonlinear generalized functions I and II

M Grosser - 2001 - books.google.com
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 …

A discontinuous Colombeau differential calculus

J Aragona, R Fernandez, SO Juriaans - Monatshefte für Mathematik, 2005 - Springer
Starting from the Colombeau Generalized Functions, the sharp topologies and the notion of
generalized points, we introduce a new kind of differential calculus (for functions between …

Renormalization of QED with planar binary trees

C Brouder, A Frabetti - The European Physical Journal C-Particles and …, 2001 - Springer
The Dyson relations between renormalized and bare photon and electron propagators
Z_3̄D(q)=D(q) and Z_2̄S(q)=S(q) are expanded over planar binary trees. This yields …

Intrinsic Characterization of Manifold‐Valued Generalized Functions

M Kunzinger, R Steinbauer… - Proceedings of the …, 2003 - Wiley Online Library
The concept of generalized functions taking values in a differentiable manifold is extended
to a functorial theory. We establish several characterization results which allow a global …

Microlocal analysis of Colombeau's generalized functions: propagation of singularities

N Dapić, S Pilipović, D Scarpalézos - Journal d'Analyse Mathématique, 1998 - Springer
We introduce the notion of pointwise regularity (̇ G^ ∞) of Colombeau's generalized
functions and give comparison theorems between ̇ G^ ∞ regularity, G^ ∞-and C∞ …

Isomorphisms of algebras of generalized functions

H Vernaeve - Monatshefte für Mathematik, 2011 - Springer
We show that for smooth manifolds X and Y, any isomorphism between the algebras of
generalized functions (in the sense of Colombeau) on X, resp. Y is given by composition …

On the foundations of nonlinear generalized functions I

E Farkas, M Grosser, M Kunzinger… - arxiv preprint math …, 1999 - arxiv.org
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically
containing the space of distributions in the sense of L. Schwartz. Employing differential …

Sheaves of nonlinear generalized functions and manifold-valued distributions

M Kunzinger, R Steinbauer, J Vickers - Transactions of the American …, 2009 - ams.org
This paper is part of an ongoing program to develop a theory of generalized differential
geometry. We consider the space $\mathcal {G}[X, Y] $ of Colombeau generalized functions …