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master's thesis
Fourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:620119
Palle, Ljudevit
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Palle, Lj. (2015). Fourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:620119

Palle, Ljudevit. "Fourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:620119

Palle, Ljudevit. "Fourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:620119

Palle, Lj. (2015). 'Fourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:620119

Palle Lj. Fourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:620119

Lj. Palle, "Fourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:620119

Metadata
TitleFourierova analiza na lokalno kompaktnim abelovim grupama i neke primjene
AuthorLjudevit Palle
MentorVjekoslav Kovač (mentor)
Committee memberVjekoslav Kovač (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberAnte Mimica (član povjerenstva)
Committee memberBoris Muha (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-07-13, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom je radu dan pregled glavnih rezultata iz Fourierove analize na lokalno kompaktnim, Abelovim grupama. Na početku je iznesen osnovni materijal iz teorije mjere, topologije i funkcionalne analize potreban za razvoj teorije na lokalno kompaktnim grupama. Potom se proučavaju Geljfandova transformacija, funkcije i konvolucija na lokalno kompaktnim grupama, reprezentacije lokalno kompaktnih grupa i funkcije pozitivnog tipa. Izneseni su i dokazani Geljfand-Raikovljev teorem, teorem o Fourierovoj inverziji i teorem o Pontrjaginovoj dualnosti, a na kraju rada se jos proučava Bohrova kompaktifikacija i primjenjuje na karakterizaciju uniformno skoro periodičnih funkcija.
Abstract (english)
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.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:620119
Study programmeTitle: Pure Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-29 09:13:27