Geodesic
On Functions Uniquely Determined by Their Asymptotic Expansion
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 4, pp. 33-48

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We present a maximal class of analytic functions. The elements of this class are uniquely determined by their asymptotic expansions. We also discuss the possibility of recovery of a function from the coefficients of its asymptotic series. In particular, we consider the problem of recovering by using Borel summation. The last published result in this direction was obtained by Alan Sokal in 1980, but his paper well known to physicists (in quantum field theory) seems to have remained unnoticed by mathematicians.
Keywords: Watson's uniqueness theorem, Gevrey expansions, Laplace transforms in complex domain, differential equations in complex domain. 
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V. P. Gurarii; D. W. H. Gillam. On Functions Uniquely Determined by Their Asymptotic Expansion. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 4, pp. 33-48. http://geodesic.mathdoc.fr/item/FAA_2006_40_4_a3/