Geodesic
Weak invertibility in weight spaces of analytic functions
Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 1061-1082

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Spaces of holomorphic functions in a disc that contain strongly invertible functions that are not weakly invertible are constructed. Moreover, criteria for weak invertibility in weight spaces of entire functions are obtained. 
@article{IM2_1996_60_5_a8,
     author = {F. A. Shamoyan},
     title = {Weak invertibility in weight spaces of analytic functions},
     journal = {Izvestiya. Mathematics },
     pages = {1061--1082},
     publisher = {mathdoc},
     volume = {60},
     number = {5},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a8/}
}
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F. A. Shamoyan. Weak invertibility in weight spaces of analytic functions. Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 1061-1082. http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a8/