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Construction of a Fourier transform based on Haar measure in structure (Rn, +, T)

Żukowicz M

Zeszyty Naukowe / Akademia Morska w Szczecinie

2014

nr 39 (111)

181--184

An important aspects of learning are the theoretical elements of mathematics and the methods of obtaining the function or designbecause it allows for further development of the issues and the ability to apply this problem in practice. The Fourier transform is very useful in science and technology. The article shows how and in what structures is possible to use the Fourier transform in the set Rn. The article describes the project of compact-open topology, which is essential to the construction of the Haar measure and integral. It was also described the concept of the nature of a locally compact topological group, because a group of characters is also essential to the construction of the Fourier transform and inverse Fourier transform. It has been proven that a group of characters is a locally compact topological group, which allows the introduction of the Haar measure. It has given an example application of the theory of Haar integral when calculating the Fourier transform for some of the electronics.