English
Related papers

Related papers: The Bohr radius and the Hadamard convolution opera…

200 papers

In this paper, we introduce the notion of the second Bohr radius for vector valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. This investigation is motivated by the work of Lev Aizenberg [Proc. Amer. Math. Soc.…

Complex Variables · Mathematics 2026-03-03 Himadri Halder

This paper is devoted to studying some mixed radial-angular integrabilities for various types of Hausdorff operators and commutators

Functional Analysis · Mathematics 2024-04-30 Ronghui Liu , Guanghui Lu

In the present paper, we provide several inequalities for the generalized numerical radius of operator matrices as introduced by A. Abu-omar and F. Kittaneh in [3]. We generalize the convexity and the log-convexity results obtained by M.…

Functional Analysis · Mathematics 2020-04-22 H. Abbas , S. Harb , H. Issa

One of the couple of translatable radii of an operator in the direction of another operator introduced in earlier work[13] is studied in details. A necessary and sufficient condition for a unit vector f to be a stationary vector of the…

Functional Analysis · Mathematics 2024-07-30 Kallol Paul

In this paper, we investigate the Bohr radius for $K$-quasiregular sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ such that the translated analytic part $h(z)-h(0)$ is quasi-subordinate to some analytic…

Complex Variables · Mathematics 2020-04-21 Ming-Sheng Liu , Saminathan Ponnusamy , Jun Wang

Recently, several authors have proved inequalities on the spectral radius $\rho$, operator norm $\|\cdot\|$ and numerical radius of Hadamard products and ordinary products of non-negative matrices that define operators on sequence spaces,…

Spectral Theory · Mathematics 2017-01-05 Aljoša Peperko

The Bohr radius for power series of holomorphic functions mapping a multidimensional Reinhardt domain into the convex domain in the complex plane is independent of this convex domain.

Complex Variables · Mathematics 2007-05-23 Lev Aizenberg

In this paper, we introduce the $f-$operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the $q-$operator radius. Properties of the newly defined radius are discussed, emphasizing how it…

Functional Analysis · Mathematics 2022-11-02 Mohammad W. Alomari , Mohammad Sababheh , Cristian Conde , Hamid Reza Moradi

We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…

Classical Analysis and ODEs · Mathematics 2015-03-17 Ricardo Almeida , Delfim F. M. Torres

In this paper, we first establish the Bohr's theorem for Ces\'aro operator defined for $f\in \mathcal{SRB}(\mathbb{B})$ of slice regular functions in the open unit ball $\mathbb{B}$ of the largest alternative division algebras of octonions…

Complex Variables · Mathematics 2025-12-12 Molla Basir Ahamed , Sabir Ahammed

In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature.…

Functional Analysis · Mathematics 2023-09-21 Mohammad Sababheh , Hamid Reza Moradi , Mohammad Alomari

In this paper, we investigate several Bohr radii associated with the Ces\'aro operator, Bernardi integral operator, $\beta$-Ces\'aro operator, and discrete Fourier transform, all defined on a set of holomorphic mappings from the unit ball…

Complex Variables · Mathematics 2026-03-18 Vasudevarao Allu , Raju Biswas , Rajib Mandal , Hiroshi Yanagihara

We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…

Functional Analysis · Mathematics 2026-02-17 Shiva Sheybani , Hamid Reza Moradi , Mohammad Sababheh

In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \begin{equation*} \Omega_{\gamma}=\bigg\{z\in\mathbb{C} :…

Complex Variables · Mathematics 2026-04-15 Molla Basir Ahamed , Vasudevarao Allu , Himadri Halder

We establish the membership criteria in terms of Hadamard product for a normalized analytic function to be in the class of infinitesimal generators. Furthermore, the embedding of various subclasses of normalized univalent functions in the…

Complex Variables · Mathematics 2022-10-25 Surya Giri , S. Sivaprasad Kumar

Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…

Complex Variables · Mathematics 2019-11-07 Chinu Singla , Sushma Gupta , Sukhjit Singh

Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\mathbf{k}[x]$. We consider…

Rings and Algebras · Mathematics 2016-01-20 Li Guo , Markus Rosenkranz , Shanghua Zheng

We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of…

Functional Analysis · Mathematics 2024-08-13 Pintu Bhunia , Santanu Bag , Kallol Paul

We develop several upper and lower bounds for the $A$-Euclidean operator radius of $2$-tuple operators admitting $A$-adjoint, and show that they refine the earlier related bounds. As an application of the bounds developed here, we obtain…

Functional Analysis · Mathematics 2024-08-14 Suvendu Jana , Pintu Bhunia , Kallol Paul

We say that a class $\mathcal{B}$ of analytic functions $f$ of the form $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if for the largest radius $R_{f}<1$, the…

Complex Variables · Mathematics 2026-04-15 Vasudevarao Allu , Himadri Halder