no. 5
Quasi-analyticity in Carleman ultraholomorphic classes
[Quasi-analyticité dans des classes ultraholomorphes de Carleman]
Lastra, Alberto1 ; Sanz, Javier1
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, Tome 60 (2010) no. 5, pp. 1629-1648.

Nous donnons une caractérisation pour deux notions différentes de quasi-analyticité dans des classes ultraholomorphes de Carleman en plusieurs variables dans des polysecteurs. En considérant des suites fortement régulières, nous établissons aussi des généralisations du lemme de Watson sous une condition additionnelle reliée à l’index de croissance de la suite.

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.

DOI : 10.5802/aif.2568
Classification : 30D60, 32A38, 32A40
Keywords: Quasi-analyticity, Carleman classes, asymptotic expansions, Watson’s Lemma
Mot clés : quasi-analyticité, classes de Carleman, développements asymptotiques, lemme de Watson
Lastra, Alberto 1 ; Sanz, Javier 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) 
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Lastra, Alberto; Sanz, Javier. Quasi-analyticity in Carleman ultraholomorphic classes. Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1629-1648. doi : 10.5802/aif.2568. http://www.numdam.org/articles/10.5802/aif.2568/

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