Demostració del teorema de convolució de Titchmarsh

Abstract

[en] The Titchmarsh Convolution Theorem is a renowned theorem on the support of the convolution on two functions, and it has several possible equivalent formulations. Within this project, we expose the details of Thomas Randsford's proof [5], based on the factorization of functions in the space $H^{\infty}$ of holomorphic and bounded functions on the disk. To reformulate the convolution problem in terms of holomorphic functions one uses the Laplace transform.