Translation induced composition semigroup on the dirichlet space of the half-plane

Key Points

• The study highlights the construction of a semigroup of composition operators on Dirichlet space.
• Determining the semigroup and spectral properties sheds light on their mathematical behavior.
• Resolvents of the infinitesimal generator are expressed as integral operators, revealing their structure.
• Norms and spectra of these resolvents provide insight into their functional characteristics.