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Aakriti Sharma

Publications and source records attributed to Aakriti Sharma.

5 recordsLinked to original sources
arXiv2026

Commutants of complex symmetric weighted composition operators on Fock space

In this paper, we investigate weighted composition operators $W_{f,g}$ commuting with complex symmetric weighted composition operators $W_{\psi, \varphi}$ on the classical Fock space $\mathcal{F}^{2}(\mathbb{C})$. In particular, we investigate the symbols $f$ and $g$ give rise to $W_{f,g}$ commuting with a complex symmetric weighted composition operator on $\mathcal{F}^{2}$. We further characterize when the commuting weighted composition operators are self-adjoint and normal.

math.FA↗
arXiv2022

Nuclear Volterra composition operators between Bloch and weighted type spaces

In this paper, we completely characterize nuclear Volterra composition operators $T^ϕ_g : \mathcal H^\infty_ν\longrightarrow \mathcal H^\infty_μ$ and $S^ϕ_g : \mathcal H^\infty_ν\longrightarrow \mathcal H^\infty_μ$ acting between weighted type spaces in terms of the symbols $g$ and $ϕ$ of $T^ϕ_g$ and $S^ϕ_g$ and weights $ν$ and $μ$, when the weights $ν$ and $μ$ are normal weights in the sense of Shields and Williams. Moreover, nuclear Volterra composition operators acting between little weighted type spaces and Bloch spaces of order $β$ are also characterized.

math.FA↗
arXiv2022

Vanishing Carleson measures and power compact weighted composition operators

In this paper, we characterize Carleson measure and vanishing Carleson measure on Bergman spaces with admissible weights in terms of {\it t-Berezin transform} and {\it averaging function} as key tools. Moreover, power bounded and power compact weighted composition operators are characterized as application of Carleson measure and vanishing Carleson measure respectively on Bergman spaces with admissible weights.

math.CV↗
arXiv2022

Compact and order bounded sum of weighted differentiation composition operators

In this paper, we characterize bounded, compact and order bounded sum of weighted differentiation composition operators from Bergman type spaces to weighted Banach spaces of analytic functions, where the sum of weighted differentiation composition operators is defined as $$ S^{n}_{\vec{u},τ}(f)= \displaystyle\sum_{j=0}^{n}D_{u_{j} ,τ}^{j}(f), \; \; f \in \mathcal{H}(\mathbb D).$$ Here $\mathcal{H}(\mathbb D)$ is the space of all holomorphic functions on $\mathbb D$, $\vec{u}=\{u_{j}\}_{j=0}^{n}$, $u_{j} \in \mathcal{H}(\mathbb{D})$, $τ$ a holomorphic self-map of $\mathbb D$, $f^{(j)}$ the $j$th derivative of $f$ and weighted differentiation composition operator $D_{u_{j},τ}^{j}$ is defined as $D_{u_{j},τ}^{j}(f)=u_{j}C_τD^{j}(f)=u_{j}f^{(j)}\circτ, \; \; f \in \mathcal{H}(\mathbb D).$

math.FA↗