Strong incompleteness of a~system of exponentials, and Macintyre's problem
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 305-318

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A solution is given for Macintyre's problem in terms of strong incompleteness of a system $\{e^{\lambda_nz}\}$, $0\lambda_n\uparrow\infty$. As a corollary it is shown that this system is incomplete in the space $C(\gamma)$, where $\gamma$ is any continuous curve.
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     author = {A. M. Gaisin},
     title = {Strong incompleteness of a~system of exponentials, and {Macintyre's} problem},
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A. M. Gaisin. Strong incompleteness of a~system of exponentials, and Macintyre's problem. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 305-318. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a0/