logo AFST
no. 4
Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 593-608. 
@article{AFST_2005_6_14_4_593_0,
     author = {Werner Balser},
     title = {Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {593--608},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {4},
     year = {2005},
     zbl = {1105.35024},
     mrnumber = {2188584},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_593_0/}
}
TY  - JOUR
AU  - Werner Balser
TI  - Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2005
SP  - 593
EP  - 608
VL  - 14
IS  - 4
PB  - Université Paul Sabatier, Institut de Mathématiques
PP  - Toulouse
UR  - https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_593_0/
LA  - en
ID  - AFST_2005_6_14_4_593_0
ER  - 
%0 Journal Article
%A Werner Balser
%T Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2005
%P 593-608
%V 14
%N 4
%I Université Paul Sabatier, Institut de Mathématiques
%C Toulouse
%U https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_593_0/
%G en
%F AFST_2005_6_14_4_593_0
Werner Balser. Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 593-608. https://afst.centre-mersenne.org/item/AFST_2005_6_14_4_593_0/

[1] Balser (W.). - From Divergent Power Series to Analytic Functions, vol. 1582 of Lecture Notes in Math, Springer Verlag, New York, (1994 ). | MR | Zbl

[2] Balser (W. ). - Divergent solutions of the heat equation: on an article of Lutz, Miyake and Schäfke, Pacific J. of Math., 188, p. 53-63 (1999). | MR | Zbl

[3] Balser (W.). - Formal power series and linear systems of meromorphic ordinary differential equations, Springer-Verlag, New York, (2000). | MR | Zbl

[4] Balser (W. ), Miyake (M.). - Summability of formal solutions of certain partial differential equations, Acta Sci. Math. (Szeged), 65, p. 543-551 (1999). | MR | Zbl

[5] Ecalle (J. ). - Les fonctions résurgentes I-II, Publ. Math. d'Orsay, Université Paris Sud, (1981).

[6] Ecalle (J. ). - Les fonctions résurgentes III, Publ. Math. d'Orsay, Université Paris Sud, (1985). | MR | Zbl

[7] Ecalle (J.). - Introduction à l'Accélération et à ses Applications, Travaux en Cours, Hermann, Paris , (1993).

[8] Lutz (D.A. ), Miyake (M.), Schäfke (R.).- On the Borel summability of divergent solutions of the heat equation, Nagoya Math. J., 154, p. 1-29 (1999). | MR | Zbl

[9] Majima (H. ). - Asymptotic Analysis for Integrable Connections with Irregular Singular Points, vol. 1075 of Lecture Notes in Math, Springer Verlag, New York, (1984 ). | MR | Zbl

[10] Miyake (M. ), Ichinobe (K.). - On the Borel summability of divergent solutions of parabolic type equations and Barnes generalized hypergeometric functions, Surikaisekikenkyusho Kokyuroku , (2000), p. 43-57. Microlocal analysis and related topics (Japanese (Kyoto, 1999). | MR | Zbl

[11] Mozo-Fernández ( J.). - Cohomology theorems for asymptotic sheaves, Tohoku Math. J. (2), 51, p. 447-460 (1999). | MR | Zbl

[12] Mozo-Fernández ( J.). - Weierstrass theorems in strong asymptotic analysis, Bull. Polish Acad. Sci. Math., 49, p. 255-268 (2001). | MR | Zbl

[13] Tougeron ( J.-C.). - Sur les ensembles semi-analytiques avec conditions Gevrey au bord, Ann. scient. Éc. Norm. Sup. , 27 (1994), p. 173-208. | Numdam | MR