Uniqueness theorems for some classes of analytic functions

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 $\operatorname{Ln}z$.