A new class of operators and a description of adjoints of composition operators
Using the reproducing kernel of the standard Hardy Hilbert space \(H^2\), the authors establish first of all an explicit formula for the adjoint of a composition operator \(C_\varphi\) on \(H^2\), with \(\varphi\) an analytic self-map of the complex open unit disk (similarly for the classically weighted Bergman Hilbert spaces \({\mathcal A}_\alpha^2\), \(\alpha>-1\)). Then they introduce a general concept of so-called multiple-valued weighted composition operators on \(H^2\). Among other things, they show that, for a rational symbol \(\varphi\), the adjoint of \(C_\varphi\) can be expressed as a multiple-valued weighted composition operator.
scientific article; zbMATH DE number 5072816