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dc.contributor.authorMOSE, Bagasa Samuel
dc.date.accessioned2021-05-07T10:42:59Z
dc.date.available2021-05-07T10:42:59Z
dc.date.issued2019
dc.identifier.urihttps://repository.maseno.ac.ke/handle/123456789/3728
dc.description.abstractSemigroups of composition operators on spaces of analytic functions have interested mathematicians for many years. The breakthrough in Hardy spaces was given by Berkson and Porta. On Bergman and Dirichlet spaces, Siskakis did extensive research whereby he determined semigroup as well as spectral properties of these operators on the unit disk. Later, other researchers like Arvanitidis, Bonyo, Blasco, Matache and others extended the work to Hardy and Bergman spaces of the unit disk and upper half plane. However, very little is known about sernigroups of weighted composition operators on Bloch spaces. In this study therefore we investigated the properties of semigroups of weighted composition operators 011 the Bloch space. In particular, we determined a semigroup of weighted composition operators on the Bloch space; investigated its semigroup properties; and determined its spectral properties on the Bloch space of the unit disk. We used the duality properties of the non reflexive Bergman space to identify a semigroup of composition operators. To obtain the semigroup properties, we employed the theory of semigroups of linear operators and functional analysis where we determined infinitesimal generator of the semigroup and established the strong continuity property. We then determined the resolvents of the infinitesimal generator which are obtained as integral operators. Using the spectral mapping theorems as well as the Hille Yosida theorem, we obtained the spectral properties of the resulting integral operators. The results of this study will indeed contribute new knowledge and we hope it will motivate further research in this area of study.en_US
dc.publisherMaseno Universityen_US
dc.titleSpectral Properties of Semigroups of Weighted Composition Operators on the Bloch Spaceen_US
dc.typeArticleen_US


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