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Multisummability and the Stokes phenomenon

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Abstract

We define elementary acceleration operators and accelero-Laplace transformations on certain classes of (germs of) hyperfunctions on ℝ. The type of accelero-Laplace transforms considered here generalizes the notion of multisum of a formal power series. We describe the corresponding Stokes phenonenon, i.e., the difference of two accelero-Laplace transforms of the same germ in different (multi-)directions, with the aid of the operators Δ +ω and Δ -ω introduced by J. Ecalle.

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References

  1. J. Ecalle, Les fonctions résurgentes. III.Publ. Math. d'Orsay, Université de Paris-Sud, Paris, 1985.

    Google Scholar 

  2. J. Ecalle, L'accélération des fonctions résurgentes.Manuscript, 1987.

  3. J. Ecalle, The acceleration operators and their applications. In:Proc. Internat. Congr. Math., Kyoto 2 (1990), 1249–1258.Springer-Verlag, 1991.

  4. B. Candelpergher, J. C. Nosmas, and F. Pham, Approche de la résurgence.Actualités Math. Hermann, Paris, 1993.

    Google Scholar 

  5. B. Malgrange Introduction aux travaux de J. Ecalle.l'Enseignement Math. 31 (1985), 261–282.

    Google Scholar 

  6. A. Cerezo, J. Chazarain, and A. Piriou, Introduction aux hyperfonctions. In: Hyperfunctions and Theoretical Physics.Lect. Notes Math. 449 1975, 1–53.

  7. A. Kaneko, Introduction to hyperfunctions.Math. and Appl., Kluwer Academic Publishers, Dordrecht, 1988.

    Google Scholar 

  8. M. Morimoto, An introduction to Sato's hyperfunctions. Translations of Math. Monographs.Am. Math. Soc., Providence, RI, 1993.

    Google Scholar 

  9. H. Komatsu, Laplace transform of hyperfunctions. A new foundation of Heaviside calculus.J. Fac. Sc. Univ. Tokyo IA 34 (1987), 805–820.

    Google Scholar 

  10. —, Operational calculus, hyperfunctions and ultradistributions.Algebraic Anal. 1 (1988), 357–372.

    Google Scholar 

  11. J. Ecalle, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac.Actualités Math., Hermann, Paris, 1992.

    Google Scholar 

  12. J. Ecalle,Alien calculus and its applications. (Cambridge University Press, to appear.)

  13. E. C. Titchmarsh, The theory of functions. 2nd edition.Oxford University Press, Oxford, 1939.

    Google Scholar 

  14. J. P. Ramis Séries divergentes et théories asymptotiques.Publ. I.R.M.A., Strasbourg, 1991.

    Google Scholar 

  15. B. Malgrange and J.-P. Ramis, Fonctions multisommables.Ann. Inst. Fourier 41 (1991), No. 3, 1–16.

    Google Scholar 

  16. B. Malgrange, Equations différentielles à coefficients polynomiaux.Progress in Math., Birkhäuser, Basel, 1991.

    Google Scholar 

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  1. G. K. Immink

    Present address: Institute of Econometrics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

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    Immink, G.K. Multisummability and the Stokes phenomenon. Journal of Dynamical and Control Systems 1, 483–534 (1995). https://doi.org/10.1007/BF02255894

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