Generalized Integral Operators and Applications

Séverine Bernard (1) , Jean-François Colombeau (2) , Antoine Delcroix (1)

1 AOC - Analyse Optimisation Controle
2 IF - Institut Fourier

We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized integral operators can be composed unrestrictedly. This leads to the definition of the exponential, and more generally entire functions, of a subclass of such operators.

Mots clés: Integral operators; kernel; generalized functions; integral transforms

Domaines: Mathématiques générales [math.GM]

Séverine Bernard, Jean-François Colombeau, Antoine Delcroix. Generalized Integral Operators and Applications. 2005. ⟨hal-00004888⟩