Generalized integral operators and Schwartz kernel type theorems |
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| Authors: | A. Delcroix |
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| Affiliation: | 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 |
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| Abstract: | In analogy to the classical Schwartz kernel theorem, we show that a large class of linear mappings admits integral kernels in the framework of Colombeau generalized functions. To do this, we introduce new spaces of generalized functions with slow growth and the corresponding adapted linear mappings. Finally, we show that, in some sense, Schwartz' result is contained in our main theorem. |
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| Keywords: | Schwartz kernel theorem Colombeau nonlinear generalized functions Integral operator Distributions |
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