Geodesic
Uniqueness theorems for some classes of analytic functions
Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 95-129.

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This work is concerned with the further application of the method of integral transforms with Mittag–Leffler kernel to the theory of infinitely differentiable functions first developed in investigations by one of the authors [1]. Here this method will be developed further to establish uniqueness theorems of the classical Denjoy–Carleman type for several general classes of functions analytic in a sector of arbitrary angle which lies on the Riemann surface $G_\infty$ of the function $\operatorname{Ln}z$. 
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M. M. Dzhrbashyan; G. S. Kocharyan. Uniqueness theorems for some classes of analytic functions. Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 95-129. http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a4/

[1] Dzhrbashyan M. M., “Rasshirenie kvazianaliticheskikh klassov Danzhua–Karlemana”, Izv. AN ArmSSR, Matematika, III:3 (1968), 171–248

[2] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

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

[4] Korenblyum B. I., “Usloviya netrivialnosti nekotorykh klassov funktsii, analiticheskikh v ugle, i problemy kvazianalitichnosti”, Dokl. AN SSSR, 166:5 (1966), 1047–1049