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Symbole Holomorphe

  • A. Meril (a1)

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Soit T un endomorphisme continu de , nous montrons qu'il existe une fonction entière S sur C n × C n telle que ζS(x, ζ) soit de type exponential sur C n avec croissance controlée uniformément lorsque x parcourt un compact de C n , de telle sorte que pour on ait

( désigne la transformée de Fourier-Borel d'une fonctionnelle analytique). Une telle fonction S sera dite un symbole holomorphe sur C n . Réciproquement nous montrons que si S est une fonctionnelle analytique, la formule précédente permet de définir un endomorphisme continu (encore noté S) de .

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References

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1. Ehrenpreis, L., Fourier analysis in several complex variables (Wiley Interscience, 1970).
2. Hormander, L., An introduction to complex analysis in several variables (Van Nostrand, Princeton, 1966).
3. Martineau, A., Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse. Math. (1963), 1164.
4. Martineau, A., Equation différentielles d'ordre infini, Bull. Soc. Math, de France 95 (1967), 109154.
5. Treves, F., Topological vector spaces, distributions and kernels (Acad. Press, New York, 1967).
6. Gay, R., Division des fonctionnelles analytiques et fonctions entières de type exponentiel, These Se. Math. Strasbourg (1976).
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Symbole Holomorphe

  • A. Meril (a1)

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