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On the superpostition of functions in carleman classes

Published online by Cambridge University Press:  17 April 2009

Mostefa Ider
Mostefa Ider
Affiliation:
Département de mathématiques et d'informatiqueUniversité de SherbrookeSherbrooke QuébecCanada J1K 2R1
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Abstract

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In this paper we deal with classes of infinitely differentiable functions known in the literature as Carleman classes. Our main result is a characterisation of those Carleman classes that are closed under superposition. This result enables us to give a complete solution to a problem that has been considered by Gevrey, Cartan and Bang.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 471 - 476
Copyright
Copyright © Australian Mathematical Society 1989

References

[1] Bang, T., On quasi-analytisk funktioner (Nyt Norclisk Forlag, Copenhagen, 1946).Google Scholar
[2] Cartan, H., Sur les classes de fonctions définies par des inégalités sur leurs dérivées successives (Actualités Scientifiques et industrielles numéro 897, 1940).Google Scholar
[3] Gevrey, M., Oeuvres complètes (Editions du Centre National de Ia recherche scientifique, Paris, 1970).Google Scholar
[4] Malliavin, P., ‘Calcul symbolique et sous algèbres de L1(G)’, Bull. Soc. Math. France 87 (1959), 181–190.Google Scholar
[5] Mandelbrojt, S., Series adhérentes, régularisation des suites, applications (Gauthier-Villars, Paris, 1952).Google Scholar
[6] Rudin, W., ‘Division in algebras of infinitely differentiable functions’, J. Math. Mech 11 (1962), 797–809.Google Scholar
[7] Siddiqi, J.A. and Ider, M., ‘Symbolic Calculus in analytic Carleman classes’, Proc. Amer. Math. Soc. 99 (1987), 347–350.CrossRefGoogle Scholar