m-Isometric Composition Operators on Discrete Spaces

In this paper we study composition operators on discrete spaces \( L^{2}(\mu ) \) $L^2(\mu )$ . We establish the classification of underlying graphs of such operators. We obtain the characterization of m-isometric composition operators such that the underlying graph has one cycle. The paper contains also the solution of the Cauchy dual subnormality problem in the class of such composition operators.