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.
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.
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
@article{AIF_2010__60_5_1629_0, author = {Lastra, Alberto and Sanz, Javier}, title = {Quasi-analyticity in {Carleman} ultraholomorphic classes}, journal = {Annales de l'Institut Fourier}, pages = {1629--1648}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {5}, year = {2010}, doi = {10.5802/aif.2568}, mrnumber = {2766226}, zbl = {1208.30035}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2568/} }
TY - JOUR AU - Lastra, Alberto AU - Sanz, Javier TI - Quasi-analyticity in Carleman ultraholomorphic classes JO - Annales de l'Institut Fourier PY - 2010 SP - 1629 EP - 1648 VL - 60 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2568/ DO - 10.5802/aif.2568 LA - en ID - AIF_2010__60_5_1629_0 ER -
%0 Journal Article %A Lastra, Alberto %A Sanz, Javier %T Quasi-analyticity in Carleman ultraholomorphic classes %J Annales de l'Institut Fourier %D 2010 %P 1629-1648 %V 60 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2568/ %R 10.5802/aif.2568 %G en %F AIF_2010__60_5_1629_0
Lastra, Alberto; Sanz, Javier. Quasi-analyticity in Carleman ultraholomorphic classes. Annales de l'Institut Fourier, Volume 60 (2010) no. 5, pp. 1629-1648. doi : 10.5802/aif.2568. https://aif.centre-mersenne.org/articles/10.5802/aif.2568/
[1] Formal power series and linear systems of meromorphic ordinary differential equations, Universitext, Springer-Verlag, New York, 2000 | MR | Zbl
[2] On strongly asymptotically developable functions and the Borel-Ritt theorem, Studia Math., Volume 133 (1999) no. 3, pp. 231-248 | MR | Zbl
[3] Étude de certains systèmes de Pfaff avec singularités, Équations différentielles et systèmes de Pfaff dans le champ complexe (Sem., Inst. Rech. Math. Avancée, Strasbourg, 1975) (Lecture Notes in Math.), Volume 712, Springer, Berlin, 1979, pp. 131-288 | MR | Zbl
[4] Quasi-analyticity for functions of several variables, Duke Math. J., Volume 38 (1971), pp. 109-115 | DOI | MR | Zbl
[5] Theorems of Sibuya-Malgrange type for Gevrey functions of several variables, Funkcial. Ekvac., Volume 32 (1989) no. 3, pp. 365-388 | MR | Zbl
[6] Desarrollos asintóticos en polisectores. Problemas de existencia y unicidad (Asymptotic expansions in polysectors. Existence and uniqueness problems), Universidad de Valladolid, Spain (1994) (Ph. D. Thesis)
[7] Gérard-Sibuya’s versus Majima’s concept of asymptotic expansion in several variables, J. Aust. Math. Soc., Volume 71 (2001) no. 1, pp. 21-35 | DOI | MR | Zbl
[8] Non-triviality conditions for certain classes of functions analytic in an angle and problem of quasianalyticity, Dokl. Akad. Nauk SSSR, Volume 166 (1966), pp. 1046-1049 | MR | Zbl
[9] Extension d’un théorème de Carleman, Ann. Inst. Fourier (Grenoble), Volume 12 (1962), pp. 627-641 | DOI | Numdam | MR | Zbl
[10] Analogues of Cartan’s decomposition theorem in asymptotic analysis, Funkcial. Ekvac., Volume 26 (1983) no. 2, pp. 131-154 | MR | Zbl
[11] Asymptotic analysis for integrable connections with irregular singular points, Lecture Notes in Mathematics, 1075, Springer-Verlag, Berlin, 1984 | MR | Zbl
[12] Séries adhérentes, régularisation des suites, applications, Gauthier-Villars, Paris, 1952 | MR | Zbl
[13] Über quasianlytische Funktionen und Bestimmtheit asymptotischer Entwickleungen, Acta Math., Volume 53 (1929) no. 1, pp. 181-266 | DOI | JFM | MR
[14] Summability in a direction of formal power series in several variables, Asymptot. Anal., Volume 29 (2002) no. 2, pp. 115-141 | MR | Zbl
[15] Extension maps in ultradifferentiable and ultraholomorphic function spaces, Studia Math., Volume 143 (2000) no. 3, pp. 221-250 | EuDML | MR | Zbl
[16] Division by flat ultradifferentiable functions and sectorial extensions, Results Math., Volume 44 (2003) no. 1-2, pp. 169-188 | MR | Zbl
[17] A theory of asymptotic series, Philos. Trans. R. Soc. Lond. Ser. A, Volume 211 (1912), pp. 279-313 | DOI | JFM
Cited by Sources: