Geodesic
On~quasianalytic noncontinuability of a~function given by a~series of exponentials
Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 245-261.

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The author showed (RZh. Mat., 1973, 2B135) that if $0\lambda_k\uparrow\infty$, $\sum_1^\infty\lambda_k^{-1}\infty$, and the index of condensation of the sequence $\{\lambda_k\}$ is equal to zero, then the function $f(z)=\sum_1^\infty a_k e^{\lambda_kz}$ cannot be continued quasianalytically across the line of convergence of the series. Results have now been obtained on noncontinuability under a stronger restriction on $\{\lambda_k\}$: $\lim\frac k{\lambda_k^\rho}\infty$, $0\rho1$. Bibliography: 9 titles. 
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A. F. Leont'ev. On~quasianalytic noncontinuability of a~function given by a~series of exponentials. Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 245-261. http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a2/

[1] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980 | MR

[2] Leontev A. F., “Ob odnom dopolnenii k teoreme Adamara”, Dokl. AN SSSR, 206:5 (1972), 1049–1051 | MR

[3] Levin B. N., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[4] Leontev A. F., “K voprosu o vosstanovlenii funktsii po izvestnym koeffitsientam ee ryada Dirikhle”, Proc. of the Conference Constructive Theory of Functions, 1971, 273–288 | MR

[5] Leontev A. F., “K voprosu o predstavlenii tselykh funktsii ryadami eksponent”, Matem. sb., 104(146):3 (1977), 371–389 | MR

[6] Leontev A. F., “O sposobakh resheniya uravneniya beskonechnogo poryadka v deistvitelnoi oblasti”, Izv. AN SSSR. Ser. matem., 34:4 (1970), 849–880 | MR

[7] Leontev A. F., Obobscheniya ryadov eksponent, Nauka, M., 1981 | MR

[8] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[9] Salinns R. B., “Functions with null moments”, Rev. Acad. Ciencias, Madrid, 49 (1955), 331–368 | MR