Adjoints of rationally induced weighted composition operators on the Hardy, Bergman and Dirichlet spaces (Q519979)

Inspired by the work of \textit{P. S. Bourdon} and \textit{J. H. Shapiro} [J. Funct. Anal. 255, No. 8, 1995--2012 (2008; Zbl 1157.47018)], the authors determine the adjoint of a weighted composition operator defined on certain Hilbert spaces of analytic functions on the disc, in the case where the symbol of the composition operator is a rational function. The case of multiplication operators is investigated first. Operators on the Hardy space, the Bergman space and the Dirichlet space are considered separately.