Analysis of Fourier Transform in _L1 Space and its Inversion
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Date
2012-01
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Addis Ababa University
Abstract
This project discusses the concept of Fourier transform of a function in Space with its
properties theorem, inversion theorem, Fourier sine and cosine transforms theorem, Plancherel’s
and Parseval’s identities theorem and the applications of Fourier transform in partial differential
equations, Shannon’s sampling theorem and Heisenberg’s inequality.
Therefore the purpose of this project is to solving certain problems in partial differential
equations like for example Heat equation, Wave equation , and Laplace equation, to solve some
complicated integrals shortly and simply, and it works in Shannon’s sampling theorem and
Heisenberg’s inequality.
This project uses some definitions and theorems as a preliminary from some real analysis and
Fourier analysis books
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Keywords
Analysis of Fourier Transform