Generalized Integral Operators and Schwartz Kernel Theorem

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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Contributor : Antoine Delcroix <>
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Antoine Delcroix. Generalized Integral Operators and Schwartz Kernel Theorem. Journal of Mathematical Analysis and Applications, Elsevier, 2005, 306 (2), pp.481-501. ⟨10.1016/j.jmaa.2005.01.006⟩. ⟨hal-01530748⟩

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