Geodesic
Solvability of convolution equation in the Gevrey class of functions analytic in a nonconvex region
Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 35-43

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In the Gevrey space $A(q)$ of functions analytic in a nonconvex bounded region in $\mathbf{C}^-$, we consider $a$ convolution operator $L$ generated by some entire functiona. A necessary and sufficient condition under which the equality $L(A(q))=A(q)$ holds is established. 
@article{MZM_1992_52_3_a3,
     author = {O. V. Gorina},
     title = {Solvability of convolution equation in the {Gevrey} class of functions analytic in a nonconvex region},
     journal = {Matemati\v{c}eskie zametki},
     pages = {35--43},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a3/}
}
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O. V. Gorina. Solvability of convolution equation in the Gevrey class of functions analytic in a nonconvex region. Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 35-43. http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a3/