J. O. Bonyo | Searcharxiv

arXiv2019

Duality of the nonreflexive Bergman space of the upper half plane and Composition groups

We identify the predual of the nonreflexive Bergman space of the upper half plane, $L_a^1(\uP,μ_{\al})$, with the little Bloch space of the upper half plane consisting of functions vanishing at $i$. We then investigate both the semigroup and spectral properties of the adjoint groups of composition operators which are naturally obtained from the duality pairing and are therefore defined on the identified predual.

math.FA↗

arXiv2019

Weighted Composition Groups on the Little Bloch space

We determine both the semigroup and spectral properties of a group of weighted composition operators on the Little Bloch space. It turns out that these are strongly continuous groups of invertible isometries on the Bloch space. We then obtain the norm and spectra of the infinitesimal generator as well as the resulting resolvents which are given as integral operators. As consequences, we complete the analysis of the adjoint composition group on the predual on the nonreflexive Bergman space, and a group of isometries associated with a specific automorphism of the upper half plane.

math.FA↗