Complex symmetric weighted composition operators on H_gamma(D)
Date of Issue2019-05-14
School of Physical and Mathematical Sciences
In this thesis, we investigate the complex symmetric structure of weighted composition operators on the Hilbert space of holomorphic functions over the open unit disk with reproducing kernels , where . In Chapter 1, we provide some key working definitions and a brief overview of the literature on the topic. Then we proceed to Chapter 2, where we give a sufficient treatment of reproducing kernels, which plays a key role in the proofs of many results presented in this thesis. In Chapter 3, we consider conjugations on which takes the form (such conjugations are also known as weighted composition conjugations) and characterize them into two classes, denoted by and . Thereafter in Chapter 4, we obtain explicit conditions for when it is -symmetric and -symmetric respectively. In Chapter 5, we conclude this thesis by discussing some possible future directions on this investigation.