Related papers: Arithmetic Bohr radius for the Minkowski space

The Riemann-Roch theorem is of utmost importance in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of…

In this paper, we analyze multi-dimensional Bohr $({\mathcal B},c)$-almost periodic type functions. The main structural characterizations for the introduced classes of Bohr $({\mathcal B},c)$-almost periodic type functions are established.…

In this paper, we study the hyperbolic geometry of noncommutative balls generated by the joint operator radius $\omega_\rho$, $\rho\in (0,\infty]$, for $n$-tuples of bounded linear operators on a Hilbert space. In particular, $\omega_1$ is…

The purpose of this article is to study Bohr inequalities involving the absolute values of the coefficients of an operator valued function. To be more specific, we establish an operator valued analogue of a classical result regarding the…

Let $\mathcal{H}$ be the class of normalized complex valued harmonic functions $ f = h + \overline{g}$ defined on the unit disk $\mathbb{D}$, where $h$ and $g$ are analytic functions with the normalization conditions $h(0) = h'(0) - 1 = 0$…

In this paper, we investigate holomorphic mappings $F$ on the unit ball $\mathbb{B}$ of a complex Banach space of the form $F(x)=f(x)x$, where $f$ is a holomorphic function on $\mathbb{B}$. First, we investigate criteria for univalence,…

Let $H(D)$ denote the space of holomorphic functions on the unit disk $D$. We characterize those radial weights $w$ on $D$, for which there exist functions $f, g \in H(D)$ such that the sum $|f| + |g|$ is equivalent to $w$. Also, we obtain…

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…

This article is concerned with the study of Mather's \beta-function associated to Birkhoff billiards. This function corresponds to the minimal average action of orbits with a prescribed rotation number and, from a different perspective, it…

This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating…

It is a classical fact, that given an arbitrary n-dimensional convex body, there exists an appropriate sequence of Minkowski symmetrizations (or Steiner symmetrizations), that converges in Hausdorff metric to a Euclidean ball. Here we…

In this paper, we study Bohr's inequality and refined versions of Bohr-Rogosinski inequalities involving Schwarz functions. Moreover, we establish a version of multidimensional analogue of Bohr inequality and Bohr-Rogosinski inequalities…

We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from $L^\infty(\mathbb B)$ to $\mathcal B$, and from $C_0(\mathbb B)$ to $\mathcal B_0$ are onto. We…

In this paper we continue the study of free holomorphic functions on the unit ball of B(H)^n, where B(H) is the algebra of all bounded linear operators on a Hilbert space H. Several classical results from complex analysis have free…

In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of starlike and convex analytic functions. We also obtain the Bohr…

The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and…

It is crucial to explore the sharp bounds of logarithmic coefficients and the Hankel determinant involving logarithmic coefficients as part of coefficient problems in various function classes. Our primary objective in this study is to…

In this article, we prove a Lichnerowicz estimate for a compact convex domain of a K\"ahler manifold whose Ricci curvature satisfies $\Ric \ge k$ for some constant $k>0$. When equality is achieved, the boundary of the domain is totally…

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order…

Recently, in arXiv:2304.07149, a bridge was made between the very active area of spaces of Lipschitz real functions on a metric space and holomorphic functions on an open subset of a Banach space. This was done by introducing and studying…