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

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