Quasi-analyticity in Carleman ultraholomorphic classes

Alberto Lastra[1]; Javier Sanz[1]

  • [1] Universidad de Valladolid Depto. de Análisis Matemático y Didáctica de la Mat. Facultad de Ciencias Paseo Prado de la Magdalena s/n 47005 Valladolid (Spain)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 5, page 1629-1648
  • ISSN: 0373-0956

Abstract

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We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of Watson’s Lemma under an additional condition related to the growth index of the sequence.

How to cite

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Lastra, Alberto, and Sanz, Javier. "Quasi-analyticity in Carleman ultraholomorphic classes." Annales de l’institut Fourier 60.5 (2010): 1629-1648. <http://eudml.org/doc/116317>.

@article{Lastra2010,
abstract = {We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of Watson’s Lemma under an additional condition related to the growth index of the sequence.},
affiliation = {Universidad de Valladolid Depto. de Análisis Matemático y Didáctica de la Mat. Facultad de Ciencias Paseo Prado de la Magdalena s/n 47005 Valladolid (Spain); Universidad de Valladolid Depto. de Análisis Matemático y Didáctica de la Mat. Facultad de Ciencias Paseo Prado de la Magdalena s/n 47005 Valladolid (Spain)},
author = {Lastra, Alberto, Sanz, Javier},
journal = {Annales de l’institut Fourier},
keywords = {Quasi-analyticity; Carleman classes; asymptotic expansions; Watson’s Lemma; quasi-analyticity; Watson's lemma},
language = {eng},
number = {5},
pages = {1629-1648},
publisher = {Association des Annales de l’institut Fourier},
title = {Quasi-analyticity in Carleman ultraholomorphic classes},
url = {http://eudml.org/doc/116317},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Lastra, Alberto
AU - Sanz, Javier
TI - Quasi-analyticity in Carleman ultraholomorphic classes
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 5
SP - 1629
EP - 1648
AB - We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of Watson’s Lemma under an additional condition related to the growth index of the sequence.
LA - eng
KW - Quasi-analyticity; Carleman classes; asymptotic expansions; Watson’s Lemma; quasi-analyticity; Watson's lemma
UR - http://eudml.org/doc/116317
ER -

References

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  9. Pierre Lelong, Extension d’un théorème de Carleman, Ann. Inst. Fourier (Grenoble) 12 (1962), 627-641 Zbl0111.08002MR137849
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  13. Alexander Ostrowski, Über quasianlytische Funktionen und Bestimmtheit asymptotischer Entwickleungen, Acta Math. 53 (1929), 181-266 Zbl55.0184.04MR1555294
  14. Javier Sanz, Summability in a direction of formal power series in several variables, Asymptot. Anal. 29 (2002), 115-141 Zbl1022.34003MR1908320
  15. Jean Schmets, Manuel Valdivia, Extension maps in ultradifferentiable and ultraholomorphic function spaces, Studia Math. 143 (2000), 221-250 Zbl0972.46013MR1815933
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