Massaneda Clares, Francesc XavierRom Escuté, Duna2024-02-282024-02-282024-01-17https://hdl.handle.net/2445/208160Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Francesc Xavier Massaneda Clares[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.52 p.application/pdfcatcc-by-nc-nd (c) Duna Rom Escuté, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/Convolucions (Matemàtica)Funcions holomorfesTransformació de LaplaceTreballs de fi de grauConvolutions (Mathematics)Holomorphic functionsLaplace transformationBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess