2023/08/25 by Molla Basir Ahamed, Ahamed, Molla Basir, Taimur Rahman +1
Mathematics · Chemistry · #Holomorphic and Operator Theory #Synthesis and Reactivity of Sulfur-Containing Compounds #Synthesis and characterization of novel inorganic/organometallic compounds
paper · pdf · doi:10.48550/arxiv.2308.13197
Let H(\mathbbD) be the class of all holomorphic functions in the unit disk \mathbbD . We aim to explore the complex symmetry exhibited by generalized weighted composition-differentiation operators, denoted as Ln, ψ, ϕ and is defined by Ln, ψ, ϕ:=∑k=1nckDk, ψk, ϕ, where ck∈ℂ for k=1, 2, …, n, where Dk, ψ, ϕf(z):=ψ(z)f(k)(ϕ(z)), f∈ A2α(\mathbbD), in the reproducing kernel Hilbert space, labeled as A2α(\mathbbD), which encompasses analytic functions defined on the unit disk \mathbbD. By deriving a condition that is both necessary and sufficient, we provide insights into the Cμ, η -symmetry exhibited by Ln, ψ, ϕ. The explicit conditions for which the operator T is Hermitian and normal are obtained through our investigation. Additionally, we conduct an in-depth analysis of the spectral properties of Ln, ψ, ϕ under the assumption of Cμ, η -symmetry and thoroughly examine the kernel of the adjoint operator of Ln, ψ, ϕ.