Thesis on Fourier analysis and the Dirichlet problem
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Date
2017-09
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Addis Ababa University
Abstract
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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Fourier analysis and the Dirichlet