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arXiv · 2312.01615

Generalized weighted composition operators on Hardy space $H^2(\mathbb{D}^n)$

Molla Basir Ahamed·Vasudevarao Allu·Taimur Rahman
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Abstract

In this paper, we explore the complex symmetrical characteristics of weighted composition operators $W_{u, v}$ and weighted composition-differentiation operators $W_{u, v, k_1, k_2, \ldots, k_n}$ on the Hardy space $H^2(\mathbb{D}^n)$ over the Polydisk $\mathbb{D}^n$, with respect to the standard conjugation $\mathcal{J}$. We specify explicit conditions that confirm the Hermitian characteristics of the operator $W_{u, v, k_1, k_2, \ldots, k_n}$ and describe the conditions necessary for it to exhibit normal behavior. Additionally, we identify the kernels of the generalized weighted composition-differentiation operators and their corresponding adjoint operators.

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Molla Basir Ahamed, Vasudevarao Allu, Taimur Rahman. 2023-12-04. Generalized weighted composition operators on Hardy space $H^2(\mathbb{D}^n)$. https://arxiv.org/abs/2312.01615

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