This article is cited in 1 paper

Spectral synthesis on the group of conformal automorphisms of the unit disc

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University, Ukraine

Abstract: 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.

UDC: 517.444

MSC: 43A45

Received: 27.08.2016

DOI: 10.4213/sm8805

 English version: Sbornik: Mathematics, 2018, 209:1, 1–34

Bibliographic databases:

• 
• 
• 
• 
• 
•