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

M. Zurro

Studia Mathematica (1997)

  • Volume: 123, Issue: 2, page 151-163
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Zurro, M.. "A new Taylor type formula and $C^∞$ extensions for asymptotically developable functions." Studia Mathematica 123.2 (1997): 151-163. <http://eudml.org/doc/216384>.

@article{Zurro1997,
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.},
author = {Zurro, M.},
journal = {Studia Mathematica},
keywords = {Taylor formula; asymptotically developable function; extension; Gevrey function},
language = {eng},
number = {2},
pages = {151-163},
title = {A new Taylor type formula and $C^∞$ extensions for asymptotically developable functions},
url = {http://eudml.org/doc/216384},
volume = {123},
year = {1997},
}

TY - JOUR
AU - Zurro, M.
TI - A new Taylor type formula and $C^∞$ extensions for asymptotically developable functions
JO - Studia Mathematica
PY - 1997
VL - 123
IS - 2
SP - 151
EP - 163
AB - 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.
LA - eng
KW - Taylor formula; asymptotically developable function; extension; Gevrey function
UR - http://eudml.org/doc/216384
ER -

References

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  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. 

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