Translation induced composition semigroup on the dirichlet space of the half-plane
F. N. Mobagi, J. O. Bonyo, George M Mocheche · Open Journal of Mathematical Analysis · 2025
We construct a semigroup of composition operators on a subspace of the Dirichlet space of the upper half-plane. We then determine both the semigroup and spectral properties of the composition semigroup. Finally, we represent the resolvents of the infinitesimal generator as integral operators and obtain their norm and spectra.