Yu. S. Linchuk
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Representation of commutants for composition operators induced by a hyperbolic linear fractional automorphisms of the unit disk
Methods Funct. Anal. Topology 14 (2008), no. 4, 361-371
We describe the commutant of the composition operator induced by a hyperbolic linear fractional transformation of the unit disk onto itself in the class of linear continuous operators which act on the space of analytic functions. Two general classes of linear continuous operators which commute with such composition operators are constructed.
Methods Funct. Anal. Topology 12 (2006), no. 4, 384-388
We study properties of operators which are left-inverses to the operator of multiplication by an independent variable in the space $\mathcal H (G)$ of functions that are analytic in an arbitrary domain $G$. This space is endowed with topology of compact convergence. A description of cyclic elements for such operators is obtained. The obtained statements generalize known results in this direction.