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Title

A new Taylor type formula and C∞ extensions for asymptotically developable functions

Authors 1

Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Ciudad Universitaria de Canto Blanco, 28049 Madrid, Spain

Abstract

The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have C∞ extensions from any subpolysector; the Gevrey case is included.

Bibliography

  1. [BBMT] J. Bonet, R. W. Braun, R. Meise and B. A. Taylor, Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions, Studia Math. 99 (1991), 155-184.
  2. [B] J. Bruna, An extension theorem of Whitney type for non quasi-analytic classes of functions, J. London Math. Soc. (2) 22 (1980), 495-505.
  3. [GS] R. Gérard et Y. Sibuya, Etude de certains systèmes de Pfaff avec singularités, in: Lecture Notes in Math. 712, Springer, 1979, 131-288.
  4. [Ha] Y. Haraoka, Theorems of Sibuya-Malgrange type for Gevrey functions of several variables, Funkcial. Ekvac. 32 (1989), 365-388.
  5. [He] J. A. Hernández, Desarrollos asintóticos en polisectores. Problemas de existencia y unicidad, Ph.D. Thesis, University of Valladodid, 1994.
  6. [K] J. M. Kantor, Classes non-quasi-analytiques et décomposition des supports des ultradistributions, An. Acad. Brasil. Ciênc. 44 (1972), 171-180.
  7. [Mj] H. Majima, Asymptotic Analysis for Integrable Connections with Irregular Singular Points, Lecture Notes in Math. 1075, Springer, 1984.
  8. [Mj1] H. Majima, On the representation of solutions of completely integrable Pfaffian systems with irregular singular points, Proc. Sem. at R.I.M.S., Kyoto University, number 483 (1981).
  9. [M] B. Malgrange, Remarques sur les équations différentielles à points singuliers irréguliers, in: Équations différentielles et systèmes de Pfaff dans le champ complexe, Lecture Notes in Math. 712, Springer, Berlin, 1979, 77-86.
  10. [Wa] W. R. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Krieger, 1976.
  11. [W1] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89.
  12. [Wi2] H. Whitney, Functions differentiable on the boundaries of regions, Ann. of Math. 35 (1934), 482-485.
  13. [Z] M. A. Zurro, Summability au plus petit terme, Studia Math. 113 (1995), 197-198.
Studia Mathematica
1997/123/2
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Pages:
151-163
Main language of publication
English
Received
1996-06-28
Accepted
1996-09-17
Published
1997
Exact and natural sciences