Geodesic
On the zeros of analytic functions belonging to Gevrey classes
Matematičeskie zametki, Tome 15 (1974) no. 6, pp. 857-863.

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For functions $f(z)\not\equiv0$, holomorphic in the unit disk $u$, infinitely differentiable in $\overline u$, and belonging to a given $\partial u$ class on partu, we establish sufficient conditions characterizing the sets $$ K_f^\infty=\{z:|z|=1,f^{(k)}(z)=0,\quad k=0,1,2,\dots\}. $$ These conditions are close to the necessary condition due to L. Carleson and substantially more precise than the conditions given by A.-M. Chollet (see [1, 2]). 
@article{MZM_1974_15_6_a3,
     author = {V. S. Korolevich and E. A. Pogorelyi},
     title = {On the zeros of analytic functions belonging to {Gevrey} classes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {857--863},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_6_a3/}
}
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V. S. Korolevich; E. A. Pogorelyi. On the zeros of analytic functions belonging to Gevrey classes. Matematičeskie zametki, Tome 15 (1974) no. 6, pp. 857-863. http://geodesic.mathdoc.fr/item/MZM_1974_15_6_a3/