2025/02/28 by Vasudevarao Allu, Allu, Vasudevarao, Sahoo, Satyajit
Computer Science · Mathematics · #47A12 #47B15 #47B32 #47B33 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2502.20875
openalex publication_date 2025/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize the weighted composition-differentiation operators D\mfn,ψ,φ acting on Hγ(\mathbbDd) over the polydisk \mathbbDd which are complex symmetric with respect to the conjugation J. We obtain necessary and sufficient conditions for D\mfn,ψ,φ to be self-adjoint. We also investigate complex symmetry of generalized weighted composition differentiation operators Mn, ψ, φ=∑j=1najDj,ψj, φ, (where aj∈ ℂ for j=1, 2, …, n) on the reproducing kernel Hilbert space Hγ(\mathbbD) of analytic functions on the unit disk \mathbbD with respect to a weighted composition conjugation Cμ, ξ. Further, we discuss the structure of self-adjoint linear composition differentiation operators. Finally, the convexity of the Berezin range of composition operator on Hγ(\mathbbD) are investigated. Additionally, geometrical interpretations have also been employed.