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

A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on ${\mathscr{H}}^{2}$ 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...