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On a notion of resurgent function of several variables. (English) Zbl 0842.32006
The purpose of this paper is to generalize the notion and basic properties of resurgent functions of one variable to several variables. There are several ways of introducing resurgent functions of one variable. The one that the authors choose to generalize is that of a \(q\)-tuplet of analytic functions defined in different angular sectors of the complex plane with a generic asymptotical expansion. Their resurgent functions are of exponential type in different conic sections of the space \(\mathbb{C}^n\). They then investigate the asymptotic behavior of these functions at infinity by embedding \(\mathbb{C}^n\) in projective space. The resurgent functions then become resurgent functions of one variable depending on \((n - 1)\) parameters. They then investigate the different representation of these functions.

MSC:
32A99 Holomorphic functions of several complex variables
32A10 Holomorphic functions of several complex variables
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
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[1] Les Fonetions Résurgents, I, II, III. Publications MalhématiquesďOrsay, 1981-1985
[2] Malrange, Ecalle. ĽEnseignement Math Ematique. 31 pp 261– (1985)
[3] St Ernin, Soviet Math. Dokl. 31 pp 125– (1985)
[4] Stkrnin, Russian Journal of Math. Phys. 1 (1992)
[5] Introduction a ĽEtude Topologique des Singularités de Landau. Gauthicr-Villars, Paris. 1967
[6] . and , Une Approache de la Résurgence. Prcpublications de ľUniversité de Nice-Sophia-Antipolis, 1991
[7] Lectures on Borel-Laplace Transformation and Resurgent Functions. 1992. Preprint
[8] St Ernin, Soviet Math. Dokl. 44 pp 496– (1991)
[9] St Ernin, Russian Acad. Sci. Izv. Math. 40 pp 67– (1993)
[10] St Ernin, Soviet Math. Dokl. 37 pp 38– (1988)
[11] and , Differential Equations on Complex Manifolds. Khmer Academic Publishers. Dordreeht. The Netherlands, 1994 · doi:10.1007/978-94-017-1259-0
[12] Sternin, Matem Zametki. 17 pp 107– (1991)
[13] Thom., Bui. A. M. S. 75 pp 240– (1969) · Zbl 0197.20502 · doi:10.1090/S0002-9904-1969-12138-5
[14] , and , Lagrangian Manifolds and the Maslov Operator. Springer-Verlag. Berlin Heidelberg New York Tokyo, 1990 · doi:10.1007/978-3-642-61259-6
[15] , and , Premiers pas en Calcul Etranger. Prepublications dc ľUniversité de Nice-Sophia-Antipolis, 1991
[16] Ramis, Springer Lecture Notes in Physics. 126 (1980)
[17] and , Elementary Acceleration and Multisommability, I. 1990. Preprint
[18] Voros, Ann. Inst. H. Poinearé. Sect A (N. S.) 39 pp 211– (1983)
[19] Schrodinger equation from O(h’) to O(h’). Path integrals from mcV to MeV. Bielfeld Encount Phys. Math., World Sci. Publ. Singapore, 7, 1986, 173–195
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