Thesis On Fourier Analysis And The Dirichlet Problem
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In this thesis, using the properties of convergence of Fourier series and some other properties of trigonometric polynomials, in particular that they are sums of holomorphic and anti-holomorphic functions, we are able to solve the Dirichlet problem on the Disc. Then, applying the result for the unit Disc along with a couple of Möbius transformations, we are able to solve the Dirichlet problem on the upper half plane
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