Majorant Series

TL;DR

This paper explores the bounds on the sum of moduli of series expansions of bounded holomorphic functions in complex variables, including new results and expository content from a symposium lecture.

Contribution

It introduces new unpublished results on the size of series term sums for bounded holomorphic functions in multiple complex variables.

Findings

New bounds for series of bounded holomorphic functions

Unpublished results with complete proofs included

Expository insights from a symposium lecture

Abstract

This article discusses questions in one and several complex variables about the size of the sum of the moduli of the terms of the series expansion of a bounded holomorphic function. Although the article is partly expository, it also includes some previously unpublished results with complete proofs. The article is based on a lecture at the third Korean several complex variables symposium held at the Global Analysis Research Center at Seoul National University in December 1998.