Bohr’s inequalities on a bounded balanced domain

Start: 5 November 2025 11:30
End: 5 November 2025 12:30
Categories: Conference , Seminar , Instituto de Matemáticas UGR

Where: Seminario Análisis Matemático, Facultad de Ciencias

IMAG Functional Analysis Seminar
Title: Bohr's inequalities on a bounded balanced domain
By Tatsuhiro Honda (Senshu University, Japan)
Abstract: In 1914, H. Bohr proved that if the power series $f(\zeta)=\sum_{j=0}^{\infty}a_j\zeta^j$ converges in $\mathbb{U}$, where (\mathbb{U}\) is the unit disc in $\mathbb{C}$, and $|f(\zeta)|<1$ holds for all $\zeta \in \mathbb{U}$, then the inequality $$\sum_{j=0}^{\infty}|a_j|r^j\leq 1$$ holds for all $\zeta$ with $|\zeta|=r\leq 1/6$. The largest $r\leq 1$ such that the above equality holds is called the Bohr radius for the unit disc case. The fact that the constant $1/3$ is best possible is showen later. In this talk, we will discuss to generalize some results about Bohr's radii for a holomorphic mapping to higher dimensional complex Banach spaces.This work is partially supported by JSPS KAKENHI Grant Number 23K03136.