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

• Autorzy: Żukowicz M
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fourier transform; Haar measure; Haar integral; compact-open topology; characters of topological group; group of characters

• Wydawca: Wydawnictwo Naukowe Akademii Morskiej w Szczecinie
• Czasopismo: Zeszyty Naukowe / Akademia Morska w Szczecinie
• Rocznik: 2014
• Tom: nr 39 (111)
• Strony: 181--184
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Żukowicz M

• Technical University of Rzeszow, Department of Computer Science and Automation

Bibliografia

• 1. ENGELKING R.: Topologia ogólna. PWN, Warszawa 1976.
• 2. PONTRIAGIN L.S.: Grupy Topologiczne. PWN, Warszawa 1961.
• 3. RYKACZEWSKI K.: Dualność Pontriagina i miara Haara. NCU, Toruń 2008.
• 4. OPIAL Z.: Algebra wyższa. PWN, Warszawa 1974.
• 5. RUDIN W.: Analiza rzeczywista i zespolona. PWN, Warszawa 1998.