In the context of a theorem of Richter, we establish a similarity between -semigroups of analytic -isometries acting on a Hilbert space and the multiplication operator semigroup induced by for in the right-half plane acting boundedly on weighted Dirichlet spaces on . As a consequence, we derive a connection with the right shift semigroup given by
acting on a weighted Lebesgue space on the half line and address some applications regarding the study of the invariant subspaces\linebreak of -semigroups of analytic 2-isometries.
Cite this article
Eva A. Gallardo-Gutiérrez, Jonathan R. Partington, -semigroups of -isometries and Dirichlet spaces. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1415–1425DOI 10.4171/RMI/1030