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dc.contributorBoza Rocho, Santiago
dc.contributor.authorSatorres Almenara, Àngel
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.description.abstractThe objective of this thesis is to make a theoretical and formal study of the Fourier Transform and to introduce some of its many applications. We start studying the Fourier Transform in L^1 and L^2, its behavior respect to the convolution and the multidimensional generalization. This study will allow us to solve, analyze and understand more two of the most well-known and important Partial Differential Equations: the Heat equation and the Wave equation. Finally, we will introduce and study the most relevant properties of filters. In order to give the most general results and exploit the full potential of the Fourier Transform, we will introduce the distributions, their basic properties and the theory of the Fourier Transform for distributions.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
dc.subject.lcshFourier analysis
dc.subject.otherFourier Transform
dc.subject.otherPartial Differential Equation
dc.subject.otherWave equation
dc.subject.otherHeat equation
dc.subject.otherSchwartz Space
dc.titleTransformada de Fourier: aplicacions a la resolució d'equacions en derivades parcials
dc.typeBachelor thesis
dc.subject.lemacFourier, Anàlisi de
dc.subject.amsClassificació AMS::42 Fourier analysis::42B Fourier analysis in several variables
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
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