On the Bohr phenomenon for complex valued and vector valued functions

TL;DR

This paper investigates the Bohr inequality for Fourier transforms of complex and vector valued functions on compact groups, linking it to the geometry of operator spaces in Hilbert spaces.

Contribution

It extends the Bohr phenomenon to Fourier transforms on compact groups and connects it with the modulus of convexity in operator spaces.

Findings

Established Bohr inequalities for Fourier transforms on compact groups

Linked the Bohr phenomenon to the modulus of convexity in operator spaces

Provided new insights into the structure of bounded linear operators

Abstract

We explore the Bohr inequality involving the Fourier transforms of complex valued integrable and square integrable functions defined on a second countable compact topological group. We also investigate the connection of the Bohr phenomenon with a modulus of convexity of the space of bounded linear operators defined on a complex Hilbert space.