Results 11 to 20 of about 188 (25)

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R) [PDF]

, 2013
MSC 2010: 46F30, 46F10Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of
Damyanov, Blagovest P.
core  

Embeddings of ultradistributions and periodic hyperfunctions in Colombeau type algebras through sequence spaces

, 2002
In a recent paper, we gave a topological description of Colombeau type algebras introducing algebras of sequences with exponential weights. Embeddings of Schwartz' spaces into the Colombeau algebra G are well known, but for ultradistribution and periodic
Delcroix, Antoine, Hasler, Maximilian F., Pilipović, Stevan, Valmorin, Vincent   +3 more
core   +1 more source

Wave-type equations of low regularity

, 2011
We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.Comment: 16 pages,
Clarke CJS, Clemens Hanel, Colombeau JF, Friedlander FG   +3 more
core   +1 more source

Kernel Theorems in Spaces of Tempered Generalized Functions

, 2006
In analogy to the classical isomorphism between $\mathcal{L}(\mathcal{S}(\mathbb{R}^{n}) ,\mathcal{S}^{\prime}(\mathbb{R}^{m}) ) $ and $\mathcal{S}^{\prime}(\mathbb{R}^{n+m}) $, we show that a large class of moderate linear mappings acting between the ...
ANTOINE DELCROIX, Antonevich, Colombeau, Colombeau, Garetto, Hörmander, Nedeljkov, Oberguggenberger, Radyno, Scarpalézos, Treves   +10 more
core   +1 more source

Basic properties of ultrafunctions

, 2013
Ultrafunctions are a particular class of functions defined on a non-Archimedean field. They provide generalized solutions to functional equations which do not have any solutions among the real functions or the distributions.
Baglini, Lorenzo Luperi, Benci, Vieri
core   +1 more source

Local regularity in non-linear generalized functions [PDF]

, 2013
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with additional ...
Pilipovic, Stevan, Scarpalezos, Dimitris, Vindas, Jasson   +2 more
core   +3 more sources

Remarks on the embedding of spaces of distributions into spaces of Colombeau generalized functions

, 2004
We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. We show that the various constructions of such embeddings existing in the literature lead in fact to the same one.Comment: 13 ...
Delcroix, A.
core   +1 more source

Hyperseries in the non-Archimedean ring of Colombeau generalized numbers. [PDF]

Mon Hefte Math, 2022
Tiwari D, Giordano P.
europepmc   +1 more source

Pointvalue characterizations in multi-parameter algebras [PDF]

We extend classical results from the Colombeau algebra, concerning point-value characterizations of generalized functions, to the more general case of multi-parameter (C,E,P)–algebras. Our investigations include considerations about different definitions
Jean-André Marti, Maximilian Hasler
core  

Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers. [PDF]

Mon Hefte Math, 2021
Mukhammadiev A, Tiwari D, Apaaboah G, Giordano P.   +3 more
europepmc   +1 more source