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Generalized Integral Operators and Applications

Published online by Cambridge University Press:  01 December 2006

SÉVERINE BERNARD ,
JEAN-FRANÇOIS COLOMBEAU  and
ANTOINE DELCROIX
SÉVERINE BERNARD
Affiliation:
Université des Antilles et de la Guyane, Laboratoire AOC, Campus de Fouillole, 97159 Pointe-à-Pitre, Guadeloupe. e-mail: severine.bernard@univ-ag.fr
JEAN-FRANÇOIS COLOMBEAU
Affiliation:
Institut Fourier, Université J. Fourier, 100 rue des Maths, BP 74, 38402 St Martin d'Heres, France. e-mail: jf.colombeau@wanadoo.fr
ANTOINE DELCROIX
Affiliation:
Université des Antilles et de la Guyane, Laboratoire AOC, Campus de Fouillole, 97159 Pointe-à-Pitre, Guadeloupe. e-mail: antoine.delcroix@univ-ag.fr
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 3 , November 2006 , pp. 521 - 546
Copyright
© 2006 Cambridge Philosophical Society

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