On quasianalytic noncontinuability of a function given by a series of exponentials

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 $\{\lambda_k\}$: $\lim\frac k{\lambda_k^\rho}<\infty$, $0<\rho<1$.
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