Kernel theorems in spaces of generalized functions

• Autorzy: Antoine Delcroix
• Języki publikacji: EN

Abstrakty

EN

In analogy to the classical isomorphism between 𝓛(𝓓(ℝⁿ), $𝓓 '(ℝ^{m}))$ and $𝓓 '(ℝ^{m+n})$ (resp. $𝓛(𝓢(ℝⁿ),𝓢'(ℝ^{m}))$ and $𝓢'(ℝ^{m+n})$), we show that a large class of moderate linear mappings acting between the space $𝒢_{C}(ℝⁿ) $ of compactly supported generalized functions and 𝒢(ℝⁿ) of generalized functions (resp. the space $𝒢_{𝓢}(ℝⁿ)$ of Colombeau rapidly decreasing generalized functions and the space $𝒢_{τ}(ℝⁿ)$ of temperate ones) admits generalized integral representations, with kernels belonging to specific regular subspaces of $𝒢(ℝ^{m+n})$ (resp. $𝒢_{τ}(ℝ^{m+n})$). The main novelty is to use accelerated δ-nets, which are unit elements for the convolution product in these regular subspaces, to construct the kernels. Finally, we establish a strong relationship between these results and the classical ones.

Kategorie tematyczne

• 45P05: Integral operators
• 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
• 47G10: Integral operators
• 46F05: Topological linear spaces of test functions, distributions and ultradistributions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 88
• Numer: 1
• Strony: 77-89

Daty

wydano

2010

Twórcy

autor

Antoine Delcroix

• Equipe Analyse Algébrique Non Linéaire, Laboratoire Analyse, Optimisation, Contrôle, Faculté des sciences - Université des Antilles et de la Guyane, 97159 Pointe-à-Pitre Cedex, Guadeloupe (France)

Identyfikatory

DOI

10.4064/bc88-0-7