Bohr's power series theorem in the Minkowski space

• DOI: 10.48550/arxiv.2309.15550
• Publication Date: 2023-01-01
• Authors: Allu, Vasudevarao; Halder, Himadri; Pal, Subhadip
• Keywords: Mathematics - Complex Variables; FOS: Mathematics; Complex Variables (math.CV); 32A05, 32A10, 32A17, 30B10

The main aim of this paper is to study the $n$-dimensional Bohr radius for holomophic functions defined on Reinhardt domain in $\mathbb{C}^n$ with positive real part. The present investigation is motivated by the work of Lev Aizenberg [Proc. Amer. Math. Soc. 128 (2000), 2611--2619]. A part of our investigation in the present paper includes a connection between the classical Bohr radius and the arithmetic Bohr radius of unit ball in the Minkowski space $\ell^n_{q}\, , 1\leq q\leq \infty$. Further, we determine the exact value of Bohr radius in terms of arithmetric Bohr radius.<br/>11 Pages<br/>