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

V. V. Volchkov   ; Vit. V. Volchkov

Sbornik. Mathematics, Tome 207 (2016) no. 7, pp. 942-963

Résumé

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.

Détail

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

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