arXiv subjects

Taimur Rahman

Publications and source records attributed to Taimur Rahman.

8 recordsLinked to original sources

arXiv2026

Bohr-Type Inequalities for Shifted Disks via Optimal $H^2$-Embeddings

The primary objective of this paper is to systematically generalize this phenomenon by replacing the standard unit disk with a family of nested, internally tangent shifted disks $\Omega_\gamma$ parameterized by $\gamma \in [0, 1)$, defined by$$\Omega_\gamma = \left\{ z \in \mathbb{C} : \left| z + \frac{\gamma}{1 - \gamma} \right| < \frac{1}{1 - \gamma},\; \gamma\in [0, 1) \right\}.$$ By exploiting the geometric characteristics of $\Omega_\gamma$ and evaluating the limiting behavior as $\gamma \to 1^-$, we establish a novel framework to determine the Bohr radius for the unbounded half-plane $\mathbb{H}_1 = \{z \in \mathbb{C} : \text{Re}(z) < 1\}$. Furthermore, we prove several sharp variations of the Bohr inequality within these domains, including refined and improved formulations for unimodular bounded analytic functions. The results obtained herein not only extend classical radius problems to unbounded regions but also illuminate the delicate interplay between domain deformation and coefficient estimates.

math.CV↗

arXiv2026

Sharp Bohr-Type Inequalities Involving Euler Operator and Area Functionals on $\mathbb{P}\Delta(0;1_n)$

In this paper, we establish several higher-dimensional generalizations of refined Bohr-type inequalities for bounded holomorphic functions mapping into the unit polydisk $\mathbb{P}\Delta(0;1_n)$ in $\mathbb{C}^n$. First, we formulate multidimensional analogues of sharp Bohr-type inequalities originally established by Liu \emph{et al.} [{\it Bull. Sci. Math.} {\bf 173} (2021) 103054], incorporating both squared coefficient terms and area functional components. Second, we provide improved inequalities for a recent multidimensional extension by Ahamed \emph{et al.} [{\it Complex Anal. Oper. Theory} {\bf 20}(6) (2026), 142] by introducing an analogous term corresponding to the area functional. Finally, we extend a refined Bohr-type inequality involving the term $\vert{}f(z)-a_0\vert{}$ to the setting of several complex variables. All the results are shown to be sharp.

math.CV↗

arXiv2025

Bohr Phenomenon for $K$-quasiconformal Harmonic Mappings Involving One Parameter

In this article, we study Bohr-type inequalities involving a parameter or convex combinations for $K$-quasiconformal, sense-preserving harmonic mappings in $\mathbb{D}$, where the analytic part is subordinate to a convex function. Moreover, we establish similar inequalities when the subordinating function is chosen from the class of concave univalent functions with pole $p$, as well as from the family of concave univalent functions with opening angle $\pi\alpha$. The results generalize several existing results.

math.CV↗

arXiv2025

Bohr inequality and Bohr-Rogosinski inequality for $K$-Quasiconformal harmonic mappings

In this paper, we prove several sharp Bohr-type and Bohr-Rogosinski-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{D}$, whose analytic part is subordinate to a function belonging to the class of concave univalent functions on $\mathbb{D}$. In addition, we derive Bohr-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{D}$, where the analytic part is subordinate to a function from the Ma-Minda class of convex and starlike functions. The results generalize several existing results.

math.CV↗

arXiv2024

VoltaVision: A Transfer Learning model for electronic component classification

In this paper, we analyze the effectiveness of transfer learning on classifying electronic components. Transfer learning reuses pre-trained models to save time and resources in building a robust classifier rather than learning from scratch. Our work introduces a lightweight CNN, coined as VoltaVision, and compares its performance against more complex models. We test the hypothesis that transferring knowledge from a similar task to our target domain yields better results than state-of-the-art models trained on general datasets. Our dataset and code for this work are available at https://github.com/AnasIshfaque/VoltaVision.

cs.CV↗

arXiv2023

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

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.

math.FA↗

arXiv2023

Complex symmetric weighted composition operators on the space $\mathcal{H}^2_2(\mathbb{D})$

In this paper, we introduce a new norm for $\mathcal{S}^2(\mathbb{D})$, encompassing functions whose first and second derivatives belong to both the Hardy space $\mathcal{H}^2(\mathbb{D})$ and the classical Bergman space $\mathcal{A}^2(\mathbb{D})$. Moreover, we present some basic properties of the space $\mathcal{H}^2_2(\mathbb{D})$ and subsequently establish conditions for symbols $\phi$ and $\Psi$ to provide $W_{\Psi, \phi}$ complex symmetric, employing a unique conjugation $\mathcal{J}$.

math.FA↗

arXiv2023

Generalized weighted composition-differentiation operators on weighted Bergman spaces

Let $ \mathcal{H}(\mathbb{D}) $ be the class of all holomorphic functions in the unit disk $ \mathbb{D} $. We aim to explore the complex symmetry exhibited by generalized weighted composition-differentiation operators, denoted as $L_{n, \psi, \phi}$ and is defined by \begin{align*} L_{n, \psi, \phi}:=\sum_{k=1}^{n}c_kD_{k, \psi_k, \phi},\; \mbox{where }\; c_k\in\mathbb{C}\; \mbox{for}\; k=1, 2, \ldots, n, \end{align*} where $ D_{k, \psi, \phi}f(z):=\psi(z)f^{(k)}(\phi(z)),\; f\in \mathcal{A}^2_{\alpha}(\mathbb{D}), $ in the reproducing kernel Hilbert space, labeled as $\mathcal{A}^2_{\alpha}(\mathbb{D})$, which encompasses analytic functions defined on the unit disk $\mathbb{D}$. By deriving a condition that is both necessary and sufficient, we provide insights into the $ C_{\mu, \eta} $-symmetry exhibited by $L_{n, \psi, \phi}$. 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 $ L_{n, \psi, \phi} $ under the assumption of $ C_{\mu, \eta} $-symmetry and thoroughly examine the kernel of the adjoint operator of $L_{n, \psi, \phi}$.

math.CV↗