Spectra of Composition Groups on the Weighted Dirichlet Space of the Upper Half-Plane

Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane

“…For the case of the upper half plane, the study of composition semigroups yielding Cesáro-type operators was initiated by [10] on the Hardy space, and later extended by [11] on the Hardy and weighted Bergman spaces. For the Dirichlet space of the upper half plane, even though the composition semigroups have been partially considered by [12], the Cesáro-type operators have not been studied. In this work we construct such an operator on a subspace of the Dirichlet space of U and determine its properties.…”