Multidimensional Bohr radii for holomorphic functions with values in complex Banach spaces

2023/08/15 by Allu, Vasudevarao, Halder, Himadri, Pal, Subhadip · 3 citations
#32A05 #32A10 #46B45 #46G20 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.07825

Abstract

The main aim of this paper is to answer certain open questions related to the exact values of multidimensional Bohr radii by using the concept of arithmetic Bohr radius for holomorphic functions defined in complete Reinhardt domains in ℂⁿ with values in complex Banach spaces. More specifically, for holomorphic functions with values in arbitrary complex Banach spaces, we explore the asymptotic estimates of the arithmetic Bohr radius in the unit ball of ℓⁿ_q (1≤ q≤ ∞) spaces. As an application, we obtain the exact value of multidimensional Bohr radius for the unit ball in ℓⁿ₁ spaces which improves the previously known result of Aizenberg.

Cited by

• Arithmetic Bohr radius and Local Banach space theory
• Local Banach Space Theoretic Approach to Bohr's Theorem for Vector Valued Holomorphic and Pluriharmonic Functions
• On multidimensional Bohr radius of finite dimensional Banach spaces

Related

• On multidimensional Bohr radii for Banach spaces
• Asymptotic value of the multidimensional Bohr radius
• On multidimensional Bohr radius of finite dimensional Banach spaces
• Multi-dimensional Bohr radii of Banach space valued holomorphic functions
• Arithmetic Bohr radius for the Minkowski space