Fourierova analiza na lokalno kompaktnim, Abelovim grupama i neke primjene

Palle, Ljudevit (2015) Fourierova analiza na lokalno kompaktnim, Abelovim grupama i neke primjene. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

This work provides an overview of the more important results in Fourier analysis on locally compact Abelian groups. At the beginning the basic material from measure theory, topology, and functional analysis is listed, as it is necessary for developing the theory on locally compact groups. Afterwards, the Gelfand transform is studied, followed by functions and convolution on locally compact groups, representations of locally compact groups, and functions of positive type. The main theorems formulated and proven in this work are: the Gelfand-Raikov theorem, the Fourier inversion theorem, and the Pontrjagin duality theorem. Finally, the Bohr compactification is investigated and applied to a characterization of uniformly almost periodic functions.

Item Type: Thesis (Diploma thesis)
Supervisor: Kovač, Vjekoslav
Date: 2015
Number of Pages: 70
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 23 Oct 2015 10:43
Last Modified: 23 Oct 2015 10:43
URI: http://digre.pmf.unizg.hr/id/eprint/4178

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