Letter to the editor: A short complex-variable proof of the Titchmarsh convolution theorem

TL;DR

This paper offers a concise proof of the Titchmarsh convolution theorem using complex analysis techniques, specifically the canonical factorization theorem for bounded holomorphic functions.

Contribution

It introduces a novel, simplified proof of the Titchmarsh convolution theorem leveraging complex-variable methods.

Findings

Provides a new proof approach for the Titchmarsh convolution theorem

Simplifies understanding of the theorem through complex analysis

Highlights the connection between convolution support and holomorphic function factorization

Abstract

The Titchmarsh convolution theorem is a celebrated result about the support of the convolution of two functions. We present a simple proof based on the canonical factorization theorem for bounded holomorphic functions on the unit disk.