# 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.

### Cyclical elements of operators which are left-inverses to multiplication by an independent variable

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.