This article is cited in 4 papers

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

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University, Ukraine

Abstract: For the group $G$ of conformal automorphisms of the unit disc the problem of spectral analysis is considered for subspaces $\mathscr{U}\subset C(G)$ which are invariant under right shifts by elements of $G$ and conjugations by elements of the rotation subgroup. It turns out that, in contrast to subspaces of $C(G)$ which are merely invariant under right shifts, $\mathscr{U}$ contains a minimal subspace with the above properties.
Bibliography: 26 titles.

Keywords: spectral analysis, conformal automorphism group, invariant subspace, Schwartz theorem.

UDC: 517.444

MSC: 43A45

Received: 29.04.2015 and 02.04.2016

DOI: 10.4213/sm8534

 English version: Sbornik: Mathematics, 2016, 207:7, 942–963

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