Composition and exponential of compactly supported generalized integral kernel operators

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 of a subclass of such operators.

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

Domaines: Mathématiques générales [math.GM]

Séverine Bernard, Jean-François Colombeau, Antoine Delcroix. Composition and exponential of compactly supported generalized integral kernel operators. 2005. ⟨hal-00004897⟩