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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     author = {A. F. Leont'ev},
     title = {On~quasianalytic noncontinuability of a~function given by a~series of exponentials},
     journal = {Izvestiya. Mathematics },
     pages = {245--261},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a2/}
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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/