30 citations · 109 across the 12 of their papers we have counts for
10 papers · 1 filter
Some properties of (C,E,P)-algebras : Overgneration and 0-order estimates
Antoine Delcroix
We give a new definition of the so-called overgenerated rings, which are the usual tool used to define the asymptotic structure of a (C,E,P)-algebra, written as a factor space M_{(…
A new approach to temperate generalized functions
Antoine Delcroix
A new approach to the algebra G_τ of temperate nonlinear generalized functions is proposed, in which G_τ is based on the space O_{M} endowed with is natural topology in contrary to…
Microlocal Asymptotic Analysis in Algebras of Generalized Functions
Antoine Delcroix, Michael Oberguggenberger, Jean-André Marti
We introduce a new type of local and microlocal asymptotic analysis in algebras of generalized functions, based on the presheaf properties of those algebras and on the properties o…
Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity
Antoine Delcroix
We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of Colombeau's simplified m…
Kernel Theorems in Spaces of Tempered Generalized Functions
Antoine Delcroix
In analogy to the classical isomorphism between and , we…
Generalized Integral Operators and Schwartz Kernel Theorem
A. Delcroix
In connection with the classical Schwartz kernel theorem, we show that in the framework of Colombeau generalized functions a large class of linear mappings admit integral kernels.…