Speaker
Description
In 1914, H. Bohr, studying Dirichlet series, discovered the following interesting fact in complex analysis, which is now called the Bohr phenomenon:
Theorem.
Let $f(z)=\sum_{n\ge 0}a_nz^n$ and $\|f\|_{\infty}:=\sup_{z\in \mathbb{D}}|f(z) |$ in the unit disc $\mathbb{D}=\{|z|<1\}$. Then
$M_rf:=\sum_{n\ge 0}^{} |a_n| r^n\le \|f\|_{\infty}, \:\:
0\le r\le 1/3.$
Moreover, the constant $1/3$ is the best possible.
We introduce the concept of the Bohr radius of a pair of operators, in terms of which many well-known results related to the Bohr inequality can be formulated. The report will discuss questions about the Bohr radius for the differential operators, Hadamard convolution operators, and other operators. Using the concept of the Bohr radius of a pair of operators, we generalize the theorem of B.Bhowmik and N.Das on the comparison of majorant series of subordinate functions.
