A generalization of the Aleksandrov operator and adjoints of weighted composition operators

Abstract

A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on H-2 by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generalization of Aleksandrov-Clark measures which corresponds to the unweighted case, that is, to the adjoint of composition operators.