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[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 …
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 …
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 …
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 …
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 …
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 …
to a functorial theory. We establish several characterization results which allow a global …
Microlocal analysis of Colombeau's generalized functions: propagation of singularities
We introduce the notion of pointwise regularity (̇ G^ ∞) of Colombeau's generalized
functions and give comparison theorems between ̇ G^ ∞ regularity, G^ ∞-and C∞ …
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 …
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 …
containing the space of distributions in the sense of L. Schwartz. Employing differential …
Sheaves of nonlinear generalized functions and manifold-valued distributions
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 …
geometry. We consider the space $\mathcal {G}[X, Y] $ of Colombeau generalized functions …