Results 1 to 10 of about 188 (25)

The Caccioppoli ultrafunctions

Advances in Nonlinear Analysis, 2017
Ultrafunctions are a particular class of functions defined on a hyperreal field ℝ∗⊃ℝ{\mathbb{R}^{\ast}\supset\mathbb{R}}. They have been introduced and studied in some previous works [2, 6, 7].
Benci Vieri, Berselli Luigi Carlo, Grisanti Carlo Romano   +2 more
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Regularity properties of distributions through sequences of functions [PDF]

, 2012
We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations $(T\ast\phi_{n})$.Comment ...
C. Garetto, Dimitris Scarpalézos, H. Triebel, J.-F. Colombeau, Jasson Vindas, L. Hörmander, M. Grosser, M. Oberguggenberger, S. Pilipović, Stevan Pilipović, Y. Meyer   +10 more
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The classical theory of calculus of variations for generalized functions

Advances in Nonlinear Analysis, 2017
We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ...
Lecke Alexander, Luperi Baglini Lorenzo, Giordano Paolo   +2 more
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Topological properties of regular generalized function algebras [PDF]

, 2010
We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 ...
A Delcroix, A Delcroix, C Garetto, C Garetto, G Hörmann, H Vernaeve, H. Vernaeve, J Aragona, N Dapić, S Pilipović   +9 more
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Classes of generalized functions with finite type regularities [PDF]

, 2012
We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the ...
C Garetto, C. Garetto, G. Hörmann, G. Hörmann, H Vernaeve, J. Vindas, L Schwartz, M Grosser, M Oberguggenberger, M. Nedeljkov, S. Pilipović, S. Pilipović, Y Meyer, Y Meyer   +13 more
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An algebraic approach to manifold-valued generalized functions

, 2011
We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth ...
A. Kriegl, Annegret Burtscher, H. Vernaeve, J. Aragona, J. Grabowski, J. Mrčun, J.F. Colombeau, J.F. Colombeau, L. Schwartz, M. Grosser, M. Kunzinger, M. Kunzinger, M. Kunzinger, M. Kunzinger, M. Kunzinger, M.W. Hirsch, N. Higson, R. Abraham   +17 more
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An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms [PDF]

, 2011
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions.
Colombeau J. F., Colombeau J. F., Folland G. B., Grosser M., Hahn H., Kaneko A., Kanwal R. P., Kaplansky I., Karunakaran V., Krull W., Levi-Civita T., Lightstone A. H., Luxemburg W. A.J., Marker D., Nedeljkov M., Oberguggenberger M., Oberguggenberger M., Schiff J. L., Todor D. Todorov, Todorov T., Vladimirov V., Waerden B. L., Zariski O.   +22 more
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Geodesic completeness of generalized space-times

, 2015
We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions.
Steinbauer, Roland, Sämann, Clemens
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SOME RESULTS ON COLOMBEAU PRODUCT OF DISTRIBUTIONS [PDF]

, 2012
In this paper some results on singular products of distributions are derived. The results are obtained in Colombeau algebra of generalized functions, which is most relevant algebraic construction for tackling nonlinear problems of Schwartz ...
JOLEVSKA-TUNESKA, BILJANA, MITEVA, MARIJA   +1 more
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Isomorphisms of algebras of Colombeau generalized functions

, 2006
We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X.
A. Delcroix, E. Zeidler, G. Hörmann, G.W. Mackey, Hans Vernaeve, I. Kolár, J. Aragona, J. Aragona, J. Grabowski, J. Mrčun, J.-F. Colombeau, J.W. Roever de, L. Schwartz, L. Schwartz, M. Grosser, M. Grosser, M. Kunzinger, M. Kunzinger, M. Kunzinger, M. Nedeljkov, M. Oberguggenberger, M. Oberguggenberger, M.W. Hirsch, N. Dapić, R. Steinbauer, R.V. Kadison   +25 more
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