Download PDF - Extension maps in ultradifferentiable and ultraholomorphic function spacesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Extension maps in ultradifferentiable and ultraholomorphic function spaces

Authors 1, 2

Affiliations

  1. Institut de Mathématique, Université de Liège, Sart Tilman Bât. B 37, B-4000 Liège 1, Belgium
  2. Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner 50, E-46100 Burjasot (Valencia), Spain

Abstract

The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for C∞-spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.

Keywords

ENG
extension map, ultradifferentiable function, Roumieu type, Beurling type

Bibliography

  1. E. Borel, Sur quelques points de la théorie des fonctions, Ann. Sci. Ecole Norm. Sup. 12 (1895), 9-55.
  2. J. C. Canille, Desenvolvimento asintotico e introduç ao as cálculo diferential resurgente, 17 Colóquio Brasileiro de Matemática, IMPA, 1989.
  3. H. Cartan, Sur les classes de fonctions définies par des inégalités portant sur leurs dérivées successives, Actualités Sci. Indust. 867, Publ. Inst. Math. Univ. Clermont-Ferrand, Hermann, Paris, 1940.
  4. A. Gorny, Contribution à l'étude de fonctions dérivables d'une variable réelle, Acta Math. 71 (1939), 317-358.
  5. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  6. L. Hörmander, The Analysis of Linear Partial Differential Operators, I, Springer, Berlin, 1983.
  7. S. Mandelbrojt, Séries Adhérentes, Régularisation des Suites, Applications, Collection de Monographies sur la Théorie des Fonctions, Gauthier-Villars, Paris, 1952.
  8. B. Mityagin, Approximate dimension and bases in nuclear spaces, Uspekhi Mat. Nauk 16 (1961), no. 4, 63-132 (in Russian); English transl.: Russian Math. Surveys 16 (1961), 59-127.
  9. H.-J. Petzsche, On E. Borel's theorem, Math. Ann. 282 (1988), 299-313.
  10. J. F. Ritt, On the derivatives of a function at a point, Ann. of Math. 18 (1916), 18-23.
  11. J. C. Tougeron, An introduction to the theory of Gevrey expansions and to the Borel-Laplace transform with some applications, Course of 3rd Cycle, Univ. of Toronto.
  12. G. Valiron, Théorie des fonctions, Masson, Paris, 1966.
Studia Mathematica
2000/143/3
Export to PBN, Opens in new tab
Pages:
221-250
Main language of publication
English
Received
1999-01-22
Accepted
1999-07-12
Published
2000
Exact and natural sciences