Results 1 to 10 of about 534 (28)
Regularity of nonlinear generalized functions: A counterexample in the nonstandard setting
Examples and Counterexamples, 2021 Regularity theory in generalized function algebras of Colombeau type is largely based on the notion of G∞-regularity, which reduces to C∞-regularity when restricted to Schwartz distributions.
H. Vernaeve
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Regularity, Local and Microlocal Analysis in Theories of Generalized Functions [PDF]
, 2007 We introduce a general context involving a presheaf A and a subpresheaf B of A. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as the B-local ...
Marti, Jean-André
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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 +13 more
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, 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 +3 more
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Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory [PDF]
, 2007 In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual $\LL(\Gc(\R^n),\wt{\C})$. After having proved the existence of a fundamental solution for a large class of partial differential operators ...
Garetto, Claudia
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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 +17 more
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An application of internal objects to microlocal analysis in generalized function algebras [PDF]
, 2016 We illustrate the use of internal objects in the nonlinear theory of generalized functions by means of an application to microlocal analysis in Colombeau algebras.Comment: 14 ...
Vernaeve, Hans
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The classical point-electron in Colombeau's theory of nonlinear generalized functions
, 2008 The electric and magnetic fields of a pole-dipole singularity attributed to a point-electron-singularity in the Maxwell field are expressed in a Colombeau algebra of generalized functions.
Andre Gsponer +3 more
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Optimal embeddings of ultradistributions into differential algebras
, 2017 We construct embeddings of spaces of non-quasianalytic ultradistributions into differential algebras enjoying optimal properties in view of a Schwartz type impossibility result, also shown in this article. We develop microlocal analysis in these algebras
Debrouwere, Andreas +2 more
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The functional analytic foundation of Colombeau algebras [PDF]
, 2013 Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications.
Nigsch, E. A.
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