Geodesic
Spectral synthesis on the group of conformal automorphisms of the unit disc
Sbornik. Mathematics, Tome 209 (2018) no. 1, pp. 1-34

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Given a group $G$ of conformal automorphisms of the unit disc $\mathbb{D}$, the problem of spectral synthesis is solved for subspaces $\mathscr{U}\subset \mathscr{E}(G)$ that are invariant under right $G$-shifts and conjugations by elements of the subgroup $\operatorname{SO}(2)$. A new theorem on spectral synthesis for subspaces of $\mathscr{E}(\mathbb{D})$ that are invariant under weighted conformal shifts is an intermediate result. Bibliography: 35 titles.
Keywords: spectral synthesis, group of conformal automorphisms, invariant subspace. 
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V. V. Volchkov; Vit. V. Volchkov. Spectral synthesis on the group of conformal automorphisms of the unit disc. Sbornik. Mathematics, Tome 209 (2018) no. 1, pp. 1-34. http://geodesic.mathdoc.fr/item/SM_2018_209_1_a0/