On strongly asymptotically developable functions and the Borel-Ritt theorem

J. Sanz; F. Galindo

Studia Mathematica (1999)

  • Volume: 133, Issue: 3, page 231-248
  • ISSN: 0039-3223

Abstract

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We show that the holomorphic functions on polysectors whose derivatives remain bounded on proper subpolysectors are precisely those strongly asymptotically developable in the sense of Majima. This fact allows us to solve two Borel-Ritt type interpolation problems from a functional-analytic viewpoint.

How to cite

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Sanz, J., and Galindo, F.. "On strongly asymptotically developable functions and the Borel-Ritt theorem." Studia Mathematica 133.3 (1999): 231-248. <http://eudml.org/doc/216615>.

@article{Sanz1999,
abstract = {We show that the holomorphic functions on polysectors whose derivatives remain bounded on proper subpolysectors are precisely those strongly asymptotically developable in the sense of Majima. This fact allows us to solve two Borel-Ritt type interpolation problems from a functional-analytic viewpoint.},
author = {Sanz, J., Galindo, F.},
journal = {Studia Mathematica},
keywords = {asymptotic expansions; Borel-Ritt theorem; holomorphic functions},
language = {eng},
number = {3},
pages = {231-248},
title = {On strongly asymptotically developable functions and the Borel-Ritt theorem},
url = {http://eudml.org/doc/216615},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Sanz, J.
AU - Galindo, F.
TI - On strongly asymptotically developable functions and the Borel-Ritt theorem
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 3
SP - 231
EP - 248
AB - We show that the holomorphic functions on polysectors whose derivatives remain bounded on proper subpolysectors are precisely those strongly asymptotically developable in the sense of Majima. This fact allows us to solve two Borel-Ritt type interpolation problems from a functional-analytic viewpoint.
LA - eng
KW - asymptotic expansions; Borel-Ritt theorem; holomorphic functions
UR - http://eudml.org/doc/216615
ER -

References

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  1. [Co] J. F. Colombeau, z A result of existence of holomorphic maps which admit a given asymptotic expansion, in: Advances in Holomorphy, J. A. Barroso (ed.), North-Holland, 1979, 221-232. 
  2. [Ha] Y. Haraoka, Theorems of Sibuya-Malgrange type for Gevrey functions of several variables, Funkcial. Ekvac. 32 (1989), 365-388. Zbl0689.32001
  3. [He] J. A. Hernández, Desarrollos asintóticos en polisectores. Problemas de existencia y unicidad, Ph.D. Thesis, University of Valladolid, 1994. 
  4. [Ho] J. Horváth, Topological Vector Spaces and Distributions, Addison-Wesley, 1966. 
  5. [Ma] H. Majima, Analogues of Cartan's decomposition theorem in asymptotic analysis, Funkcial. Ekvac. 26 (1983), 131-154. Zbl0533.32001
  6. [Ma2] H. Majima, Asymptotic Analysis for Integrable Connections with Irregular Singular Points, Lecture Notes in Math. 1075, Springer, Berlin, 1984. Zbl0546.58003
  7. [Ol] F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974. 
  8. [Wa] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Dover, New York, 1987. 
  9. [Zu] M. A. Zurro, A new Taylor type formula and C ∞ extensions for asymptotically developable functions, Studia Math. 123 (1997), 151-163. Zbl0887.58002

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