Generalized Integral Operators and Applications

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...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2006-11, Vol.141 (3), p.521-546
Hauptverfasser: BERNARD, SÉVERINE, COLOMBEAU, JEAN-FRANÇOIS, DELCROIX, ANTOINE
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004106009327