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Fourier Transform and Differential Equations

  • B. Malgrange
Part of the Mathematical Physics Studies book series (MPST, volume 12)

Summary

We study, in the complex domain, the action of the Fourier transform on the solutions of ordinary linear differential equations with polynomial coefficients. In the classical “Laplace method”, there are some restrictions; also, some choice of integration contours seem rather unsystematic. We show how to remove these restrictions and how to make these choices in a more systematic way.

Keywords

Exact Sequence Asymptotic Expansion Exponential Type Complex Domain Polynomial Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Litterature

  1. [Ca]
    Candelpergher B. — Une introduction à la résurgence,Gazette des Mathématiciens, Soc. Math. Fr., 42 (1989), 36–64.MathSciNetzbMATHGoogle Scholar
  2. [E]
    Ecalle J. — Les fonctions résurgentes,vol. I to III, Publications mathématiques d’Orsay, 1981–85.Google Scholar
  3. [I]
    Ince E.L.. — Ordinary differential equations, Dover, New-York, 1956.Google Scholar
  4. [Ka]
    Kashiwara M. — Systems of microdifferential equations, Progress in math., Birkhaüser, 1983.zbMATHGoogle Scholar
  5. [Ko]
    Komatsu H. — Operational calculus, hyperfunctions, and ultradistributions, Algebraic analysis (papers dedicated to M. Sato ), Academic Press (1988), 357–372.Google Scholar
  6. [Ma 1]
    Malgrange B. — Introduction aux travaux de J. Ecalle,l’Enseignement mathématique, 31 (1985), 261–282.Google Scholar
  7. [Ma 2]
    Malgrange B. — Equations différentielles linéaires et transformation de Fourier, Ensaios Matemâticos, vol. 1, Soc. Brasil de Matemâtica, 1989.Google Scholar
  8. [Ma 3]
    Malgrange B. — Systèmes holonomes à une variable,(book, to be published).Google Scholar
  9. [Ma 4]
    Malgrange B. — Sur les points singuliers des équations différentielles, l’Enseignement mathématique, 20 fasc.1–2 (1974), 147–176.Google Scholar
  10. [Ra]
    Ramis J.-P. — Dévissage Gevrey,Astérisque, 59–60 (1978), 173–204.Google Scholar
  11. [Ro]
    Rolba P. — Lemme de Hensel pour des opérateurs différentiels,l’Enseignement mathématique, 26 fasc. 3–4 (1980), 279–311.Google Scholar
  12. [S-K-K]
    Sato M., Kawai T., Kashiwara M. — Hyperfunctions and pseudodifferential equations,Lect. Notes in Math., 287 (1973), 265–529, Springer-Verlag.Google Scholar
  13. [W]
    Wasow W. — Asymptotic expansions for ordinary differential equations, Interscience publishers, 1965.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • B. Malgrange
    • 1
  1. 1.Institut FourierUniversité de Grenoble 1France

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