Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations

Werner Balser

Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)

  • Volume: 14, Issue: 4, page 593-608
  • ISSN: 0240-2963

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Balser, Werner. "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 14.4 (2005): 593-608. <http://eudml.org/doc/73659>.

@article{Balser2005,
author = {Balser, Werner},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Borel transform; Laplace transform},
language = {eng},
number = {4},
pages = {593-608},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations},
url = {http://eudml.org/doc/73659},
volume = {14},
year = {2005},
}

TY - JOUR
AU - Balser, Werner
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
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 4
SP - 593
EP - 608
LA - eng
KW - Borel transform; Laplace transform
UR - http://eudml.org/doc/73659
ER -

References

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  1. [1] Balser ( W.). — From Divergent Power Series to Analytic Functions, vol. 1582 of Lecture Notes in Math, Springer Verlag, New York, (1994 ). Zbl0810.34046MR1317343
  2. [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). Zbl0960.35045MR1680415
  3. [3] Balser ( W.). — Formal power series and linear systems of meromorphic ordinary differential equations, Springer-Verlag, New York, (2000). Zbl0942.34004MR1722871
  4. [4] Balser ( W. ), Miyake ( M.). — Summability of formal solutions of certain partial differential equations, Acta Sci. Math. (Szeged), 65, p. 543-551 (1999). Zbl0987.35032MR1737270
  5. [5] Ecalle ( J. ). — Les fonctions résurgentes I-II, Publ. Math. d'Orsay, Université Paris Sud, (1981). 
  6. [6] Ecalle ( J. ). - Les fonctions résurgentes III, Publ. Math. d'Orsay, Université Paris Sud, (1985). Zbl0602.30029MR852210
  7. [7] Ecalle ( J.). — Introduction à l'Accélération et à ses Applications, Travaux en Cours, Hermann, Paris , (1993). 
  8. [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). Zbl0958.35061MR1689170
  9. [9] Majima ( H. ). — Asymptotic Analysis for Integrable Connections with Irregular Singular Points, vol. 1075 of Lecture Notes in Math, Springer Verlag, New York, (1984 ). Zbl0546.58003MR757897
  10. [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). Zbl0969.35512MR1799123
  11. [11] Mozo-Fernández ( J.). — Cohomology theorems for asymptotic sheaves, Tohoku Math. J. (2), 51, p. 447-460 (1999). Zbl0959.32018MR1725621
  12. [12] Mozo-Fernández ( J.). - Weierstrass theorems in strong asymptotic analysis, Bull. Polish Acad. Sci. Math., 49, p. 255-268 (2001). Zbl0988.54019MR1863264
  13. [13] Tougeron ( J.-C.). — Sur les ensembles semi-analytiques avec conditions Gevrey au bord, Ann. scient. Éc. Norm. Sup. , 27 (1994), p. 173-208. MR1266469

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